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Seminar on Geometric Complex Analysis
Seminar information archive ～03/06｜Next seminar｜Future seminars 03/07～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
Seminar information archive
2025/01/06
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
https://u-tokyo-ac-jp.zoom.us/j/87229568765
Yongpan Zou (Univ. of Tokyo)
Positivity of twisted direct image sheaves (English)
[ Abstract ]
For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
[ Reference URL ]For a projective surjective morphism $f: X \to Y$ of complex manifolds with connected fibers, let $L$ be a line bundle on $X$. We are interested in the direct image $f_*(K_{X/Y} \otimes L)$. In general, the positivity of the bundle $L$ induces positivity in the direct image sheaves. Specifically, when $L$ is a big and nef line bundle, the vector bundle $f_*(K_{X/Y} \otimes L)$ is big. This is joint work with Y. Watanabe.
https://u-tokyo-ac-jp.zoom.us/j/87229568765
2024/12/23
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Junjiro Noguchi (The Univ. of Tokyo)
Hyperbolicity and sections in a ramified cover over abelian varieties
with trace zero (Japanese)
[ Abstract ]
We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
[ Reference URL ]We discuss a higher dimensional generalization of the Manin-Grauert Theorem ('63/'65) in relation with the function field analogue of Lang's conjecture on the finiteness of rational points in a Kobayashi hyperbolic algebraic variety over a number field. Let $B$ be a possibly open algebraic curve over $\mathbf{C}$, and let $\pi:X \to B$ be a smooth or normal projective fiber space. In '81 I proved such theorems for $\dim \geq 1$, assuming the ampleness of the cotangent bundle $T^*(X_t)$, and in '85 the Kobayashi hyperbolicity of $X_t$ with some boundary condition (BC) (hyperbolic embedding condition relative over $\bar{B}$).
It is interesting to study if (BC) is really necessary or not. If $\dim X_t=1$, (BC) is automatically satisfied, and if $T^*(X_t)$ is ample, (BC) is not necessary; thus in those cases, (BC) is unnecessary. Lately, Xie-Yuan in arXiv '23 obtained such a result without (BC) for $X$ which is a hyperbolic finite cover of an abelian variety $A/B$.
The aim of this talk is to present a simplified treatment of the Xie-Yuan theorem from the viewpoint of Kobayashi hyperbolic geometry. In particular, if the $K/\mathbf{C}$-trace $Tr(A/B)=0$ with $K=\mathbf{C}(B)$, there are only finitely many $X(K)$-points or sections in $X \to B$. In this case, Bartsch-Javanpeykar in arXiv '24 gave another proof based on Parshin's topological rigidity theorem ('90). We will discuss the proof which is based on the Kobayashi hyperbolicity.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
https://forms.gle/gTP8qNZwPyQyxjTj8
Laurent Stolovitch (Universite Cote d'Azur)
CR singularities and dynamical systems (English)
[ Abstract ]
In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
[ Reference URL ]In this talk, we'll survey some recent results done since the seminal work of Moser and Webster about smooth real analytic surfaces in $C^2$ which are totally real everywhere but at a point where the tangent space is a complex line. Such a point is called a singularity of the Cauchy-Riemann structure. We are interested in the holomorphic classification of these surface near the singularity. It happens that there is a deep connection with holomorphic classification of some holomorphic dynamical systems near a fixed point so that new results for the later provide new result for the former.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/09
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshiaki Suzuki (Niigata Univ.)
The spectrum of the Folland-Stein operator on some Heisenberg Bieberbach manifolds (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/12/02
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Hideki Miyachi (Kanazawa Univ.)
Dualities in the $L^1$ and $L^\infty$-geometries in Teichm\”uller space (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/18
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yusaku Tiba (Ochanomizu Univ.)
Polarizations and convergences of holomorphic sections on the tangent bundle of a Bohr-Sommerfeld Lagrangian submanifold (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/11/11
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Takahiro Inayama (Tokyo University of Science)
Singular Nakano positivity of direct image sheaves (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/28
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Yoshihiko Matsumoto (Osaka Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/21
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Atsushi Hayashimoto (National Institute of Technology Nagano College)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/10/07
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shinichi Tajima (Niigata Univ.)
. (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Shinichi Tajima (Niigata Univ.)
. (Japanese)
[ Abstract ]
.
[ Reference URL ].
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/07/08
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Tomoyuki Hisamoto (Tokyo Metropolitan Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Tomoyuki Hisamoto (Tokyo Metropolitan Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/06/24
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Kazumasa Narita (Nagoya Univ.)
. (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/06/17
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuta Kusakabe (Kyushu Univ.)
Oka tubes in holomorphic line bundles (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/06/10
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Katsusuke Nabeshima (Tokyo Univ. of Science)
Computing Noetherian operators of polynomial ideals
--How to characterize a polynomial ideal by partial differential operators -- (Japanese)
[ Abstract ]
Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
[ Reference URL ]Describing ideals in polynomial rings by using systems of differential operators in one of the major approaches to study them. In 1916, F.S. Macaulay brought the notion of an inverse system, a system of differential conditions that describes an ideal. In 1937, W. Groebner mentioned the importance of the Macaulay's inverse system in the study of linear differential equations with constant coefficient, and in 1938, he introduced differential operators to characterize ideals that are primary to a rational maximal ideal. After that the important results and the terminology came from L. Ehrenpreise and V. P. Palamodov in 1961 and 1970, that is the characterization of primary ideals by the differential operators. The differential operators allow one to characterize the primary ideal by differential conditions on the associated characteristic variety. The differential operators are called Noetherian operators.
In this talk, we consider Noetherian operators in the context of symbolic computation. Upon utilizing the theory of holonomic D-modules, we present a new computational method of Noetherian operators associated to a polynomial ideal. The computational method that consists mainly of linear algebra techniques is given for computing them. Moreover, as applications, new computational methods of polynomial ideals are discussed by utilizing the Noetherian operators.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/27
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Taiji Marugame (The Univ. of Electro-Communications)
Hyperkähler ambient metrics associated with twistor CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/20
10:50-12:20 Room #128 (Graduate School of Math. Sci. Bldg.)
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
https://forms.gle/gTP8qNZwPyQyxjTj8
Lijie Sun (Yamaguchi Univ.)
Kähler metrics in the Siegel domain (Japanese)
[ Abstract ]
The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
[ Reference URL ]The Siegel domain is endowed with an intrinsic Kähler structure, making it an exemplary model for the complex hyperbolic plane. Its boundary, characterized as the one-point compactification of the Heisenberg group, plays an important role in studying the geometry of the Siegel domain. In this talk, using the CR structure of the Heisenberg group we introduce a variety of Kähler structures within the Siegel domain. We conclude by demonstrating that all these metrics are PCR-Kähler equivalent, that is, essentially the same when confined to the CR structure. This talk is based on a joint work with Ioannis Platis and Joonhyung Kim.
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/05/13
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yu Kawakami (Kanazawa Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yu Kawakami (Kanazawa Univ.)
(Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/04/22
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Takayuki Koike (Osaka Metropolitan Univ.)
Neighborhood of a compact curve whose intersection matrix has a positive eigenvalue (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Takayuki Koike (Osaka Metropolitan Univ.)
Neighborhood of a compact curve whose intersection matrix has a positive eigenvalue (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2024/04/15
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yuya Takeuchi (Tsukuba Univ.)
Kohn-Rossi cohomology of spherical CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
Yuya Takeuchi (Tsukuba Univ.)
Kohn-Rossi cohomology of spherical CR manifolds (Japanese)
[ Reference URL ]
https://forms.gle/gTP8qNZwPyQyxjTj8
2023/12/11
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryo Matsuda (Kyoto Univeristy)
On Partial deformations and Bers embedding (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Ryo Matsuda (Kyoto Univeristy)
On Partial deformations and Bers embedding (Japanese)
[ Abstract ]
The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.
[ Reference URL ]The Teichmüller space of the Riemann surface S is the space of deformations of the complex structure of S. For complex analysis on Teich(S), it is biholomorphic embedded into a bounded set of the space of complex Banach spaces, denoted as B(S). This embedding is known as the Bers embedding. Additionally, when S is of infinite type, considering partial deformations can reveal properties of Teich(S). Earle-Gardiner-Lakic prove that asymptotically conformal deformations correspond to subspaces where the norm of the embedding decays at infinity. In this talk, we generalize this result, showing that deformations that become asymptotically conformal at some end correspond to spaces where the norm decays at that end. Finally, using this result and the David map, a generalization of quasiconformal maps, I’ll give that in the Bers boundary of infinite-type Riemann surface satisfying the Shiga condition, Maximal cusps are not dense.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/11/27
11:00-12:30 Room #128 (Graduate School of Math. Sci. Bldg.)
Satoshi Ogawa (Osaka Metropolitan University)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Satoshi Ogawa (Osaka Metropolitan University)
On a holomorphic tubular neighborhood of a compact complex curve and Brjuno condition (Japanese)
[ Abstract ]
Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
[ Reference URL ]Let $C$ be a compact complex curve holomorphically embedded in a non-singular complex surface $M$ with a unitary flat normal bundle $N_{C/M}$ and let $\mathcal{U}$ be a finite open cover of $C$. Gong--Stolovitch posed a sufficient condition for the existence of a holomorphic tubular neighborhood of $C$ in $M$ expressed with operator norms of Čech coboundary maps $\delta$ on $\check{C}^0(\mathcal{U}, \mathcal{O}_C(N_{C/M}^\nu))$ and $\check{C}^0(\mathcal{U}, \mathcal{O}_C(T_C \otimes N_{C/M}^\nu))$.
In this talk, we introduce some estimates of the operator norms of $\delta$. As a result, we see the Brjuno condition appears as a sufficient condition for the existence of a holomorphic tubular neighborhood.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/10/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Shin-Ichi Matsumura (Tohoku Univeristy)
The Nonvanishing problem for varieties with nef anticanonical bundle
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Shin-Ichi Matsumura (Tohoku Univeristy)
The Nonvanishing problem for varieties with nef anticanonical bundle
[ Abstract ]
In the framework of the minimal model program for generalized pairs, the abundance conjecture does not hold. However, interestingly, the generalized nonvanishing conjecture is expected to hold. This conjecture asks whether the canonical divisor of generalized pairs can be represented by an effective divisor in its numerical class. In this talk, we discuss the nonvanishing conjecture for generalized LC pairs in three dimensions and prove that the conjecture is true for the nef anti-canonical divisors.
This talk is based on joint work with V. Lazic, Th. Peternell, N. Tsakanikas, and Z. Xie.
[ Reference URL ]In the framework of the minimal model program for generalized pairs, the abundance conjecture does not hold. However, interestingly, the generalized nonvanishing conjecture is expected to hold. This conjecture asks whether the canonical divisor of generalized pairs can be represented by an effective divisor in its numerical class. In this talk, we discuss the nonvanishing conjecture for generalized LC pairs in three dimensions and prove that the conjecture is true for the nef anti-canonical divisors.
This talk is based on joint work with V. Lazic, Th. Peternell, N. Tsakanikas, and Z. Xie.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/10/16
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Hajime Tsuji (Sophia University)
The limit of Kähler-Ricci flows
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Hajime Tsuji (Sophia University)
The limit of Kähler-Ricci flows
[ Abstract ]
In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.
[ Reference URL ]In this talk, I would like to present the (normalized) limit of Kähler-Ricci flows for compact Kähler manifolds with intermediate Kodaira dimesion under the condition that the canonical bundle is abundant.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/07/10
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ken-Ichi Yoshikawa (Kyoto University)
Degenerations of Riemann surfaces and small eigenvalues of the Laplacian (日本語)
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Ken-Ichi Yoshikawa (Kyoto University)
Degenerations of Riemann surfaces and small eigenvalues of the Laplacian (日本語)
[ Abstract ]
In this talk, we consider a proper surjective holomorphic map from a smooth projective surface to a compact Riemann surface. Near a singular fiber, this is viewed as a one-parameter degeneration of compact Riemann surfaces. We fix a Kähler metric on the projective surface and consider the Kähler metric on the fibers induced from this metric. In this setting, for each regular fiber, we can consider the Laplacian acting on the functions on the fiber. It is known that for any k, the k-th eigenvalue of the Laplacian extends to a continuous function on the base curve. In particular, if the singular fiber is not irreducible, some eigenvalues of the Laplacian of the regular fiber converge to zero as the regular fiber approaches to the singular fiber. We call such eigenvalues small eigenvalues. In this talk, when the singular fiber is reduced, we will explain the asymptotic behavior of the product of all small eigenvalues of the Laplacian.
[ Reference URL ]In this talk, we consider a proper surjective holomorphic map from a smooth projective surface to a compact Riemann surface. Near a singular fiber, this is viewed as a one-parameter degeneration of compact Riemann surfaces. We fix a Kähler metric on the projective surface and consider the Kähler metric on the fibers induced from this metric. In this setting, for each regular fiber, we can consider the Laplacian acting on the functions on the fiber. It is known that for any k, the k-th eigenvalue of the Laplacian extends to a continuous function on the base curve. In particular, if the singular fiber is not irreducible, some eigenvalues of the Laplacian of the regular fiber converge to zero as the regular fiber approaches to the singular fiber. We call such eigenvalues small eigenvalues. In this talk, when the singular fiber is reduced, we will explain the asymptotic behavior of the product of all small eigenvalues of the Laplacian.
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
2023/07/03
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Katsutoshi Yamanoi (Osaka University)
Hyperbolicity and fundamental groups of complex quasi-projective varieties
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Katsutoshi Yamanoi (Osaka University)
Hyperbolicity and fundamental groups of complex quasi-projective varieties
[ Abstract ]
This talk is based on a joint work with Benoit Cadorel and Ya Deng. arXiv:2212.12225
[ Reference URL ]This talk is based on a joint work with Benoit Cadorel and Ya Deng. arXiv:2212.12225
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
