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複素解析幾何セミナー
過去の記録 ～01/24｜次回の予定｜今後の予定 01/25～
| 開催情報 | 月曜日 10:30～12:00 数理科学研究科棟(駒場) 128号室 |
|---|---|
| 担当者 | 平地 健吾, 高山 茂晴 |
過去の記録
2015年10月26日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
松本 和子 氏 (東京理科大学)
The Fubini-distance functions to pseudoconvex domains in $\mathbb{C}\mathbb{P}^2$ (Japanese)
[ 講演概要 ]
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.
In this talk, we would like to present two explicit formulas for the Levi forms of the Fubini-Study distance functions to complex or real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. This is the first step for us to approach the non-existence conjecture of Levi-flat real hypersurfaces in $\mathbb{C}\mathbb{P}^2$. We would like to also discuss a certain important quantity found in the formulas.
2015年10月19日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
森脇 淳 氏 (京都大学)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
森脇 淳 氏 (京都大学)
Semiample invertible sheaves with semipositive continuous hermitian metrics (Japanese)
[ 講演概要 ]
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
Let $(L,h)$ be a pair of a semi ample invertible sheaf and a semipositive continuous hermitian metric on a proper algebraic variety over $C$. In this talk, we would like to present the result that $(L, h)$ has the extension property, answering a generalization of a question of S. Zhang. Moreover, we consider its non-archimedean analogue.
2015年10月05日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
丸亀 泰二 氏 (東京大学)
On the volume expansion of the Blaschke metric on strictly convex domains
丸亀 泰二 氏 (東京大学)
On the volume expansion of the Blaschke metric on strictly convex domains
[ 講演概要 ]
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
The Blaschke metric is a projectively invariant metric on a strictly convex domain in a projective manifold, which is a real analogue of the complete Kahler-Einstein metric on strictly pseudoconvex domains. We consider the asymptotic expansion of the volume of subdomains and construct a global conformal invariant of the boundary. We also give some variational formulas under a deformation of the domain.
2015年09月28日(月)
10:30-12:00 数理科学研究科棟(駒場) 128号室
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
後藤 竜司 氏 (大阪大学)
Flat structures on moduli spaces of generalized complex surfaces
[ 講演概要 ]
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
The 2 dimensional complex projective space $P^2$ is rigid as a complex manifold, however $P^2$ admits 2 dimensional moduli spaces of generalized complex structures which has a torsion free flat connection on a open strata. We show that logarithmic generalized complex structure with smooth elliptic curve as type changing loci has unobstructed deformations which are parametrized by an open set of the second de Rham cohomology group of the complement of type changing loci. Then we will construct moduli spaces of generalized del Pezzo surfaces. We further investigate deformations of logarithmic generalized complex structures in the cases of type changing loci with singularities. By using types of singularities, we obtain a stratification of moduli spaces of generalized complex structures on complex surfaces and it turns out that each strata corresponding to nodes admits a flat torsion free connection.
2015年07月13日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
松本 佳彦 氏 (東京工業大学)
$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains
松本 佳彦 氏 (東京工業大学)
$L^2$ cohomology and deformation of Einstein metrics on strictly pseudo convex domains
[ 講演概要 ]
Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.
Consider a bounded domain of a Stein manifold, with strictly pseudo convex smooth boundary, endowed with an ACH-Kähler metric (examples being domains of $\mathbb{C}^n$ with their Bergman metrics or Cheng-Yau’s Einstein metrics). We give a vanishing theorem on the $L^2$ $\overline{\partial}$-cohomology group with values in the holomorphic tangent bundle. As an application, Einstein perturbations of the Cheng-Yau metric are discussed.
2015年07月06日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
児玉 秋雄 氏
On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)
児玉 秋雄 氏
On the structure of holomorphic automorphism groups of generalized complex ellipsoids and generalized Hartogs triangles (JAPANESE)
[ 講演概要 ]
In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.
In this talk, we first review the structure of holomorphic automorphism groups of generalized complex ellipsoids and, as an application of this, we clarify completely the structure of generalized Hartogs triangles. Finally, if possible, I will mention some known results on proper holomorphic self-mappings of generalized complex ellipsoids, generalized Hartogs triangles, and discuss a related question to these results.
2015年06月29日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
鈴木 雄大 氏 (東京大学)
Cohomology Formula for Obstructions to Asymptotic Chow semistability (JAPANESE)
鈴木 雄大 氏 (東京大学)
Cohomology Formula for Obstructions to Asymptotic Chow semistability (JAPANESE)
[ 講演概要 ]
Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. We generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.
Odaka and Wang proved the intersection formula for the Donaldson-Futaki invariant. We generalize this result for the higher Futaki invariants which are obstructions to asymptotic Chow semistability.
2015年06月22日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
田邊 晋 氏 (Université Galatasaray)
Amoebas and Horn hypergeometric functions
田邊 晋 氏 (Université Galatasaray)
Amoebas and Horn hypergeometric functions
[ 講演概要 ]
Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.
There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the
analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.
As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.
This is a collaboration with Timur Sadykov.
Since 10 years, the utility of the Horn hypergeometric functions in Algebraic Geometry has been recognized in a small circle of specialists. The main reason for this interest lies in the fact that every period integral of an affine non-degenerate complete intersection variety can be described as a Horn hypergeometric function (HGF). Therefore the monodromy of the middle dimensional homology can be calculated as the monodromy of an Horn HGF’s.
There is a slight difference between the Gel’fand-Kapranov-Zelevinski HGF’s and the Horn HGF’s. The latter may contain so called “persistent polynomial solutions” that cannot be mapped to GKZ HGF’s via a natural isomorphism between two spaces of HGF’s. In this talk, I will review basic facts on the Horn HGF’s. As a main tool to study the topology of the discriminant loci together with the
analytic aspects of the story, amoebas – image by the log map of the discriminant- will be highlighted.
As an application of this theory the following theorem can be established. For a bivariate Horn HGF system, its monodromy invariant space is always one dimensional if and only if its Ore-Sato polygon is either a zonotope or a Minkowski sum of a triangle and some segments.
This is a collaboration with Timur Sadykov.
2015年06月15日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
早乙女 飛成 氏
The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)
早乙女 飛成 氏
The Lyapunov-Schmidt reduction for the CR Yamabe equation on the Heisenberg group (Japanese)
[ 講演概要 ]
We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.
We will study CR Yamabe equation for a CR structure on the Heisenberg group which is deformed from the standard structure. By using Lyapunov-Schmidt reduction, it is shown that the perturbation of the standard CR Yamabe solution is a solution to the deformed CR Yamabe equation, under certain conditions of the deformation.
2015年06月08日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
糟谷 久矢 氏 (東京工業大学)
Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)
糟谷 久矢 氏 (東京工業大学)
Mixed Hodge structures and Sullivan's minimal models of Sasakian manifolds (Japanese)
[ 講演概要 ]
By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.
By the result of Deligne, Griffiths, Morgan and Sullivan, the Malcev completion of the fundamental group of a compact Kahler manifold is quadratically presented. This fact gives good advances in "Kahler group problem" (Which groups can be the fundamental groups of compact Kahler manifolds?) In this talk, we consider the fundamental groups of compact Sasakian manifolds. We show that the Malcev Lie algebra of the fundamental group of a compact 2n+1-dimensional Sasakian manifold with n >= 2 admits a quadratic presentation by using Morgan's bigradings of Sullivan's minimal models of mixed-Hodge diagrams.
2015年05月25日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
久本 智之 氏 (名古屋大学)
On uniform K-stability (Japanese)
久本 智之 氏 (名古屋大学)
On uniform K-stability (Japanese)
[ 講演概要 ]
It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.
It is a joint work with Sébastien Boucksom and Mattias Jonsson. We first introduce functionals on the space of test configurations, as non-Archimedean analogues of classical functionals on the space of Kähler metrics. Then, uniform K-stability is defined as a counterpart of K-energy's coercivity condition. Finally, reproving and strengthening Y. Odaka's results, we study uniform K-stability of Kähler-Einstein manifolds.
2015年05月18日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
足立 真訓 氏 (東京理科大学)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
足立 真訓 氏 (東京理科大学)
On a global estimate of the Diederich–Fornaess index of Levi-flat real hypersurfaces (Japanese)
[ 講演概要 ]
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.
We give yet another proof for a global estimate of the Diederich-Fornaess index of relatively compact domains with Levi-flat boundary, namely, the index must be smaller than or equal to the reciprocal of the dimension of the ambient space. Although the Diederich-Fornaess index is originally defined for relatively compact domains in complex manifolds, our formulation reveals that it makes sense for abstract Levi-flat CR manifolds.
2015年05月11日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
平地 健吾 氏 (東京大学)
Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles
平地 健吾 氏 (東京大学)
Integral Kahler Invariants and the Bergman kernel asymptotics for line bundles
[ 講演概要 ]
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one forms, which do not contribute to the integral. We apply this decomposition formula to describe the asymptotic expansion of the Bergman kernel for positive line bundles and to show that the CR Q-curvature on a Sasakian manifold is a divergence. This is a joint work with Spyros Alexakis (U Toronto).
On a compact Kahler manifold, one can define global invariants by integrating local invariants of the metric. Assume that a global invariant thus obtained depends only on the Kahler class. Then we show that the integrand can be decomposed into a Chern polynomial (the integrand of a Chern number) and divergences of one forms, which do not contribute to the integral. We apply this decomposition formula to describe the asymptotic expansion of the Bergman kernel for positive line bundles and to show that the CR Q-curvature on a Sasakian manifold is a divergence. This is a joint work with Spyros Alexakis (U Toronto).
2015年04月27日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
濱野 佐知子 氏 (福島大学)
Variational formulas for canonical differentials and application (Japanese)
濱野 佐知子 氏 (福島大学)
Variational formulas for canonical differentials and application (Japanese)
[ 講演概要 ]
We prove the variational formulas of the second order for $L_1$- and $L_0$-canonical differentials, which with the remarkable contrast are our first example in the case of the deforming non-planar open Riemann surface. As a direct application, we show the rigidity of the Euclidean radius of the moduli disk on open torus under pseudoconvexity. The main part of this talk is a joint work with Masakazu Shiba and Hiroshi Yamaguchi.
We prove the variational formulas of the second order for $L_1$- and $L_0$-canonical differentials, which with the remarkable contrast are our first example in the case of the deforming non-planar open Riemann surface. As a direct application, we show the rigidity of the Euclidean radius of the moduli disk on open torus under pseudoconvexity. The main part of this talk is a joint work with Masakazu Shiba and Hiroshi Yamaguchi.
2015年04月20日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
二木 昭人 氏 (東京大学)
Weighted Laplacians on real and complex complete metric measure spaces (Japanese)
二木 昭人 氏 (東京大学)
Weighted Laplacians on real and complex complete metric measure spaces (Japanese)
[ 講演概要 ]
We compare the weighted Laplacians on real and complex (K¥"ahler) metric measure spaces. In the compact case K¥"ahler metric measure spaces are considered on Fano manifolds for the study of K¥"ahler Ricci solitons while real metric measure spaces are considered with Bakry-¥'Emery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.
We compare the weighted Laplacians on real and complex (K¥"ahler) metric measure spaces. In the compact case K¥"ahler metric measure spaces are considered on Fano manifolds for the study of K¥"ahler Ricci solitons while real metric measure spaces are considered with Bakry-¥'Emery Ricci tensor. There are twisted Laplacians which are useful in both cases but look alike each other. We see that if we consider noncompact complete manifolds significant differences appear.
2015年04月13日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
安福 悠 氏 (日本大学)
Campana's Multiplicity and Integral Points on P^2 (English)
安福 悠 氏 (日本大学)
Campana's Multiplicity and Integral Points on P^2 (English)
[ 講演概要 ]
We analyze when the complements of (possibly reducible) curves in P^2 have Zariski-dense integral points. The analysis utilizes the structure theories for affine surfaces based on logarithmic Kodaira dimension. When the log Kodaira dimension is one, an important role is played by Campana's multiplicity divisors for fibrations, but there are some subtleties. This is a joint work with Aaron Levin (Michigan State).
We analyze when the complements of (possibly reducible) curves in P^2 have Zariski-dense integral points. The analysis utilizes the structure theories for affine surfaces based on logarithmic Kodaira dimension. When the log Kodaira dimension is one, an important role is played by Campana's multiplicity divisors for fibrations, but there are some subtleties. This is a joint work with Aaron Levin (Michigan State).
2015年04月06日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
吉川 謙一 氏 (京都大学)
Analytic torsion for K3 surfaces with involution (Japanese)
吉川 謙一 氏 (京都大学)
Analytic torsion for K3 surfaces with involution (Japanese)
[ 講演概要 ]
In 2004, I introduced a holomorphic torsion invariant for 2-elementary K3 surfaces, i.e., K3 surfaces with involution. In the talk, I will report a recent progress in this invariant. Namely, for all possible deformation types, the holomorphic torsion invariant viewed as a function on the moduli space, is expressed as the product of an explicit Borcherds lift and an explicit Siegel modular form. If time permits, I will interpret the result in terms of the BCOV invariant, i.e., the genus-one string amplitude in B-model, for Calabi-Yau threefolds of Borcea-Voisin. This is a joint work with Shouhei Ma.
In 2004, I introduced a holomorphic torsion invariant for 2-elementary K3 surfaces, i.e., K3 surfaces with involution. In the talk, I will report a recent progress in this invariant. Namely, for all possible deformation types, the holomorphic torsion invariant viewed as a function on the moduli space, is expressed as the product of an explicit Borcherds lift and an explicit Siegel modular form. If time permits, I will interpret the result in terms of the BCOV invariant, i.e., the genus-one string amplitude in B-model, for Calabi-Yau threefolds of Borcea-Voisin. This is a joint work with Shouhei Ma.
2015年02月02日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
野口潤次郎 氏 (東京大学)
Inverse of an Abelian Integral on open Riemann Surfaces and a Proof of Behnke-Stein's Theorem
[ 講演概要 ]
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
Let $X$ be an open Riemann surface and let $\Omega \Subset X$ be a relatively compact domain of $X$. We firstly introduce a scalar function $\rho(a, \Omega)>0$ for $a \in \Omega$ by means of an Abelian integral, which is a sort of convergence radius of the inverse of the Abelian integral, and heuristically measures the distance from $a$ to the boundary $\partial \Omega$. We prove a theorem of Cartan-Thullen type with $\rho(a, \Omega)$ for a holomorphically convex hull $\hat{K}_\Omega$ of a compact subset $K \Subset \Omega$; in particular, $-\log \rho(a, \Omega)$ is a continuous subharmonic function in $\Omega$. Secondly, we give another proof of Behnke-Stein's Theorem (the Steiness of $X$), one of the most basic facts in the theory of Riemann surfaces, by making use of the obtained theorem of Cartan--Thullen type with $\rho(a, \Omega)$, and Oka's Jôku-Ikô together with Grauert's Finiteness Theorem which is now a rather easy consequence of Oka-Cartan's Fundamental Theorem, particularly in one dimensional case.
2015年01月26日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
荒川智匡 氏 (上智大学)
On the uniform birationality of the pluriadjoint maps (Japanese)
[ 講演概要 ]
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
In this talk, we investigate higher dimensional polarized manifolds by using singular hermitian metrics and multiplier ideal sheaves. In particular, we show the uniform birationality of the pluriadjoint maps.
2015年01月19日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
山口博史 氏 (滋賀大学 名誉教授)
Hyperbolic span and pseudoconvexity (Japanese)
山口博史 氏 (滋賀大学 名誉教授)
Hyperbolic span and pseudoconvexity (Japanese)
[ 講演概要 ]
We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.
We show that the hyperbolic span for open torus (which is introduced by M. Shiba in 1993) has the intimate relation with the pseudoconvexity.
2014年12月15日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
辻 元 氏 (上智大学)
The limits of Kähler-Ricci flows
辻 元 氏 (上智大学)
The limits of Kähler-Ricci flows
[ 講演概要 ]
ケーラー・リッチ流を、離散化することで、その極限を解析する。
ケーラー・リッチ流を、離散化することで、その極限を解析する。
2014年12月08日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
泊 昌孝 氏 (日本大学)
擬斉次2次元正規特異点および星型特異点の極大イデアルサイクルと基本サイクルについて(都丸正氏との共同研究) (JAPANESE)
泊 昌孝 氏 (日本大学)
擬斉次2次元正規特異点および星型特異点の極大イデアルサイクルと基本サイクルについて(都丸正氏との共同研究) (JAPANESE)
2014年12月01日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
大沢健夫 氏 (名古屋大学)
Effective and noneffective extension theorems (Japanese)
大沢健夫 氏 (名古屋大学)
Effective and noneffective extension theorems (Japanese)
[ 講演概要 ]
As an effective extension theorem, I will review the sharp $L^2$ extension theorem explaining the ideas of its proofs due to Blocki and Guan-Zhou. A new proof using the Poincare metric with be given, too. As a noneffective extension theorem, I will talk about an extension theorem from semipositive divisors. It is obtained as an application of an isomorphism theorem which is essentially contained in my master thesis.
As an effective extension theorem, I will review the sharp $L^2$ extension theorem explaining the ideas of its proofs due to Blocki and Guan-Zhou. A new proof using the Poincare metric with be given, too. As a noneffective extension theorem, I will talk about an extension theorem from semipositive divisors. It is obtained as an application of an isomorphism theorem which is essentially contained in my master thesis.
2014年11月17日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
新田泰文 氏 (東京工業大学)
On strong K-stability of polarized algebraic manifolds (JAPANESE)
新田泰文 氏 (東京工業大学)
On strong K-stability of polarized algebraic manifolds (JAPANESE)
2014年11月10日(月)
10:30-12:00 数理科学研究科棟(駒場) 126号室
千葉 優作 氏 (東工大理工)
多重劣調和関数の凸なレベル集合とモンジュ・アンペールカレントの台について (JAPANESE)
千葉 優作 氏 (東工大理工)
多重劣調和関数の凸なレベル集合とモンジュ・アンペールカレントの台について (JAPANESE)
[ 講演概要 ]
In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.
In this talk, we study a geometric property of a continuous plurisubharmonic function which is a solution of the Monge-Ampere equation and has a convex level set. By using our results and Lempert's results, we show a relation between the supports of the Monge-Ampere currents and complex $k$-extreme points of closed balls for the Kobayashi distance in a bounded convex domain in $C^n$.
