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過去の記録 ～03/27｜次回の予定｜今後の予定 03/28～
| 開催情報 | 火曜日 10:30～11:30 or 12:00 数理科学研究科棟(駒場) ハイブリッド開催/002号室 |
|---|---|
| 担当者 | 權業 善範・中村 勇哉・田中公 |
過去の記録
2012年01月30日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
権業 善範 氏 (東京大学数理科学研究科)
On varieties of globally F-regular type (JAPANESE)
権業 善範 氏 (東京大学数理科学研究科)
On varieties of globally F-regular type (JAPANESE)
[ 講演概要 ]
I will talk about recent topics on varieties of globally F-regular type.
I will talk about recent topics on varieties of globally F-regular type.
2012年01月23日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
山田 紀美子 氏 (岡山理科大学理学部)
Sigularities and Kodaira dimension of the moduli of stable sheaves on Enriques surfaces (JAPANESE)
山田 紀美子 氏 (岡山理科大学理学部)
Sigularities and Kodaira dimension of the moduli of stable sheaves on Enriques surfaces (JAPANESE)
[ 講演概要 ]
We shall estimate singularities of moduli of stable sheaves on Enriques/hyper-elliptic surfaces via the Kuranishi theory, consider when its singularities are canonical, and calculate its Kodaira dimension.
We shall estimate singularities of moduli of stable sheaves on Enriques/hyper-elliptic surfaces via the Kuranishi theory, consider when its singularities are canonical, and calculate its Kodaira dimension.
2012年01月16日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
中止になりました
Mihai Paun 氏 (Institut Élie Cartan and KIAS)
TBA(中止になりました) (JAPANESE)
中止になりました
Mihai Paun 氏 (Institut Élie Cartan and KIAS)
TBA(中止になりました) (JAPANESE)
2011年12月26日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
岡田拓三 氏 (京都大学大学大学院理学研究科)
Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)
岡田拓三 氏 (京都大学大学大学院理学研究科)
Birational unboundedness of Q-Fano varieties and rationally connected strict Mori fiber spaces (JAPANESE)
[ 講演概要 ]
It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.
It has been known that suitably restricted classes of Q-Fano varieties are bounded. I will talk about the birational unboundedness of (log terminal) Q-Fano varieties with Picard number one and of rationally connected strict Mori fiber spaces in each dimension $¥geq 3$. I will explain the idea of the proof which will be done after passing to a positive characteristic.
2011年12月12日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
都合により中止となりました。
Robert Laterveer 氏 (CNRS, IRMA, Université de Strasbourg)
A version of Barth's theorem for singular varieties (中止になりました) (JAPANESE)
都合により中止となりました。
Robert Laterveer 氏 (CNRS, IRMA, Université de Strasbourg)
A version of Barth's theorem for singular varieties (中止になりました) (JAPANESE)
2011年12月05日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
那須 弘和 氏 (東海大学理学部情報数理学科)
Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)
那須 弘和 氏 (東海大学理学部情報数理学科)
Obstructions to deforming curves on a uniruled 3-fold (JAPANESE)
[ 講演概要 ]
In this talk, I review some results from a joint work with Mukai:
1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and
2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.
As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.
In this talk, I review some results from a joint work with Mukai:
1. a generalization of Mumford's example of a non-reduced component of the Hilbert scheme, and
2. a sufficient condition for a first order deformation of a curve on a uniruled 3-fold to be obstructed.
As a sequel of the study, we will discuss some obstructed deformations of degenerate curves on a higher dimensional scroll.
2011年12月01日(木)
16:30-18:00 数理科学研究科棟(駒場) 002号室
Dmitry Kaledin 氏 (Steklov Mathematics Institute/ KIAS)
Cyclic K-theory (ENGLISH)
Dmitry Kaledin 氏 (Steklov Mathematics Institute/ KIAS)
Cyclic K-theory (ENGLISH)
[ 講演概要 ]
Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.
Cyclic K-theory is a variant of algebraic K-theory introduced by Goodwillie 25 years ago and more-or-less forgotten by now. I will try to convince the audience that cyclic K-theory is actually quite useful -- in particular, it can be effectively computed for varieties over a finite field.
2011年11月28日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
川谷康太郎 氏 (京都大学大学院理学研究科)
Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)
川谷康太郎 氏 (京都大学大学院理学研究科)
Comparison with Gieseker stability and slope stability via Bridgeland's stability (JAPANESE)
[ 講演概要 ]
In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.
In this talk we compare two classical notions of stability (Gieseker stability and slope stability) for sheaves on K3 surfaces by using stability conditions which was introduced by Bridgeland. As a consequence of this work, we give a classification of 2 dimensional moduli spaces of sheaves on K3 surface depending on the rank of the sheaves.
2011年11月14日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
渡辺 究 氏 (東京大学数理科学研究科)
On projective manifolds swept out by cubic varieties (JAPANESE)
渡辺 究 氏 (東京大学数理科学研究科)
On projective manifolds swept out by cubic varieties (JAPANESE)
[ 講演概要 ]
The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.
The structures of embedded complex projective manifolds swept out by varieties with preassigned properties have been studied by several authors. In this talk, we study structures of embedded projective manifolds swept out by cubic varieties.
2011年11月07日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
伊藤 敦 氏 (東京大学数理科学研究科)
Okounkov bodies and Seshadri constants (JAPANESE)
伊藤 敦 氏 (東京大学数理科学研究科)
Okounkov bodies and Seshadri constants (JAPANESE)
[ 講演概要 ]
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.
Okounkov bodies, which are convex bodies associated to big line bundles, have rich information of the line bundles. On the other hand, Seshadri constants are invariants which measure the positivities of line bundles. In this talk, I will explain a relation between Okounkov bodies and Seshadri constants.
2011年10月31日(月)
15:30-17:00 数理科学研究科棟(駒場) 122号室
藤野 修 氏 (京都大学理学系研究科)
Minimal model theory for log surfaces (JAPANESE)
藤野 修 氏 (京都大学理学系研究科)
Minimal model theory for log surfaces (JAPANESE)
[ 講演概要 ]
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.
We discuss the log minimal model theory for log sur- faces. We show that the log minimal model program, the finite generation of log canonical rings, and the log abundance theorem for log surfaces hold true under assumptions weaker than the usual framework of the log minimal model theory.
2011年07月04日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
永井 保成 氏 (早稲田大学理工学術院基幹理工学部数学科)
Birational Geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification (JAPANESE)
永井 保成 氏 (早稲田大学理工学術院基幹理工学部数学科)
Birational Geometry of O'Grady's six dimensional example over the Donaldson-Uhlenbeck compactification (JAPANESE)
[ 講演概要 ]
O'Grady constructed two sporadic examples of compact irreducible symplectic Kaehler manifold, by resolving singular moduli spaces of sheaves on a K3 surface or an abelian surface. We will give a full description of the birational geometry of O'Grady's six dimensional example over the corresponding Donaldson-Uhlenbeck compactification, using an explicit calculation of certain kind of GIT quotients.
If time permits, we will also discuss an involution of the example induced by a Fourier-Mukai transformation.
O'Grady constructed two sporadic examples of compact irreducible symplectic Kaehler manifold, by resolving singular moduli spaces of sheaves on a K3 surface or an abelian surface. We will give a full description of the birational geometry of O'Grady's six dimensional example over the corresponding Donaldson-Uhlenbeck compactification, using an explicit calculation of certain kind of GIT quotients.
If time permits, we will also discuss an involution of the example induced by a Fourier-Mukai transformation.
2011年06月27日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Vladimir Lazić 氏 (Imperial College London)
MMP revisited, II (ENGLISH)
Vladimir Lazić 氏 (Imperial College London)
MMP revisited, II (ENGLISH)
[ 講演概要 ]
I will talk about how finite generation of certain adjoint rings implies everything we currently know about the MMP. This is joint work with A. Corti.
I will talk about how finite generation of certain adjoint rings implies everything we currently know about the MMP. This is joint work with A. Corti.
2011年06月07日(火)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Chenyang Xu 氏 (MIT)
Log canonical closure (ENGLISH)
Chenyang Xu 氏 (MIT)
Log canonical closure (ENGLISH)
[ 講演概要 ]
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
(joint with Christopher Hacon) In this talk, we will address the problem on given a log canonical variety, how we compactify it. Our approach is via MMP. The result has a few applications. Especially I will explain the one on the moduli of stable schemes.
If time permits, I will also talk about how a similar approach can be applied to give a proof of the existence of log canonical flips and a conjecture due to Kollár on the geometry of log centers.
2011年06月06日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
石井 志保子 氏 (東京大学数理科学研究科)
Multiplier ideals via Mather discrepancies (JAPANESE)
石井 志保子 氏 (東京大学数理科学研究科)
Multiplier ideals via Mather discrepancies (JAPANESE)
[ 講演概要 ]
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
For an arbitrary variety we define a multiplier ideal by using Mather discrepancy.
This ideal coincides with the usual multiplier ideal if the variety is normal and complete intersection.
In the talk I will show a local vanishing theorem for this ideal and as corollaries we obtain restriction theorem, subadditivity theorem, Skoda type theorem, and Briancon-Skoda type theorem.
2011年05月30日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
Jungkai Alfred Chen 氏 (National Taiwan University and RIMS)
Kodaira Dimension of Irregular Varieties (ENGLISH)
[ 講演概要 ]
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
$f:X\\to Y$ be an algebraic fiber space with generic geometric fiber $F$, $\\dim X=n$ and $\\dim Y=m$. Then Iitaka's $C_{n,m}$ conjecture states $$\\kappa (X)\\geq \\kappa (Y)+\\kappa (F).$$ In particular, if $X$ is a variety with $\\kappa(X)=0$ and $f: X \\to Y$ is the Albanese map, then Ueno conjecture that $\\kappa(F)=0$. One can regard Ueno’s conjecture an important test case of Iitaka’s conjecture in general.
These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno’s conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
2011年05月23日(月)
17:00-18:30 数理科学研究科棟(駒場) 126号室
佐野 友二 氏 (熊本大学大学院自然科学研究科)
Alpha invariant and K-stability of Fano varieties (JAPANESE)
佐野 友二 氏 (熊本大学大学院自然科学研究科)
Alpha invariant and K-stability of Fano varieties (JAPANESE)
[ 講演概要 ]
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).
From the results of Tian, it is proved that the lower bounds of alpha invariant implies K-stability of Fano manifolds via the existence of Kähler-Einstein metrics. In this talk, I will give a direct proof of this relation in algebro-geometric way without using Kähler-Einstein metrics. This is joint work with Yuji Odaka (RIMS).
2011年05月16日(月)
17:00-18:30 数理科学研究科棟(駒場) 126号室
大川 新之介 氏 (東京大学数理科学研究科)
On images of Mori dream spaces (JAPANESE)
大川 新之介 氏 (東京大学数理科学研究科)
On images of Mori dream spaces (JAPANESE)
[ 講演概要 ]
Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.
The purpose of this talk is to study the image of a morphism from a MDS.
Firstly I prove that such an image again is a MDS.
Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.
This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.
The point is that these results can be clearly explained via the VGIT description for MDS.
If I have time, I touch on generalizations and an application to the Shokurov polytopes.
Mori dream space (MDS), introduced by Y. Hu and S. Keel, is a class of varieties whose geometry can be controlled via the VGIT of the Cox ring. It is a generalization of both toric varieties and log Fano varieties.
The purpose of this talk is to study the image of a morphism from a MDS.
Firstly I prove that such an image again is a MDS.
Secondly I introduce a fan structure on the effective cone of a MDS and show that the fan of the image coincides with the restriction of that of the source.
This fan encodes some information of the Zariski decompositions, which turns out to be equivalent to the information of the GIT equivalence. In toric case, this fan coincides with the so called GKZ decomposition.
The point is that these results can be clearly explained via the VGIT description for MDS.
If I have time, I touch on generalizations and an application to the Shokurov polytopes.
2011年05月09日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
上原 北斗 氏 (首都大学東京大学院理工学研究科)
Fourier--Mukai partners of elliptic ruled surfaces (JAPANESE)
上原 北斗 氏 (首都大学東京大学院理工学研究科)
Fourier--Mukai partners of elliptic ruled surfaces (JAPANESE)
[ 講演概要 ]
Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.
We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.
Atiyah classifies vector bundles on elliptic curves E over an algebraically closed field of any characteristic. On the other hand, a rank 2 vector bundle on E defines a surface S with P^1-bundle structure on E.
We study when S has an elliptic fibration according to the Atiyah's classification. As its application, we determines the set of Fourier--Mukai partners of elliptic ruled surfaces over the complex number field.
2011年05月02日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
古川 勝久 氏 (早稲田大学大学院基幹理工学研究科)
Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)
古川 勝久 氏 (早稲田大学大学院基幹理工学研究科)
Projective varieties admitting an embedding with Gauss map of rank zero (JAPANESE)
[ 講演概要 ]
本講演では, 楫 元・深澤 知両氏と共同でおこなったタイトルに述べた研究と,それにつづく最近の研究について発表する.
研究の対象となるのは, 正標数においてあらわれる階数の退化するガウス写像であり、特に、その極端な場合のものを (GMRZ) と名付け考察する.正確には, 射影多様体 $X$ がつぎの性質をもつとき (GMRZ) を満たすと定義する:
「ある埋込み $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ が存在し,そのガウス写像 $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ の一般点での階数が零となる.」
本研究では、特に $X$ に有理曲線 $C$ がのっている場合を考察し、「その normal bundle $N_{C/X}$ の $¥mathbb{P}^1$ 上の分解型に (GMRZ) の性質が遺伝する」という基本定理を得た.ひとつの結果としては,標数$2$の三次フェルマー型超曲面の (GMRZ)による特徴付けを得た.講演のなかでは、blow-up と (GMRZ) の関係などについても説明したい.
本講演では, 楫 元・深澤 知両氏と共同でおこなったタイトルに述べた研究と,それにつづく最近の研究について発表する.
研究の対象となるのは, 正標数においてあらわれる階数の退化するガウス写像であり、特に、その極端な場合のものを (GMRZ) と名付け考察する.正確には, 射影多様体 $X$ がつぎの性質をもつとき (GMRZ) を満たすと定義する:
「ある埋込み $¥iota: X ¥hookrightarrow ¥mathbb{P}^M$ が存在し,そのガウス写像 $X ¥dashrightarrow G(¥dim(X), ¥mathbb{P}^M)$ の一般点での階数が零となる.」
本研究では、特に $X$ に有理曲線 $C$ がのっている場合を考察し、「その normal bundle $N_{C/X}$ の $¥mathbb{P}^1$ 上の分解型に (GMRZ) の性質が遺伝する」という基本定理を得た.ひとつの結果としては,標数$2$の三次フェルマー型超曲面の (GMRZ)による特徴付けを得た.講演のなかでは、blow-up と (GMRZ) の関係などについても説明したい.
2011年04月25日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
高木 寛通 氏 (東京大学数理科学研究科)
Mirror symmetry and projective geometry of Reye congruences (JAPANESE)
高木 寛通 氏 (東京大学数理科学研究科)
Mirror symmetry and projective geometry of Reye congruences (JAPANESE)
[ 講演概要 ]
This is a joint work with Shinobu Hosono.
It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).
Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.
For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in
P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check
that X and Y are not birational each other.
Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.
Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.
This is a joint work with Shinobu Hosono.
It is well-known that the projective dual of the second Veronese variety v_2(P^n) is the symmetric determinantal hypersurface H. However, in the context of homological projective duality after Kuznetsov, it is natural to consider that the Chow^2 P^n and H are dual (note that Chow^2 P^n is the secant variety of v_2(P^n)).
Though we did not yet formulate what this duality exactly means in full generality, we show some results in this context for the values n¥leq 4.
For example, let n=4. We consider Chow^2 P^4 in P(S^2 V) and H in P(S^2 V^*), where V is the vector space such that P^4 =P(V). Take a general 4-plane P in
P(S^2 V^*) and let P' be the orthogonal space to P in P(S^2 V). Then X:=Chow^2 P^4 ¥cap P' is a smooth Calabi-Yau 3-fold, and there exists a natural double cover Y -> H¥cap P with a smooth Calabi-Yau 3-fold Y. It is easy to check
that X and Y are not birational each other.
Our main result asserts the derived equivalence of X and Y. This derived equivalence is given by the Fourier Mukai functor D(X)-> D(Y) whose kernel is the ideal sheaf in X×Y of a flat family of curves on Y parameterized by X.
Curves on Y in this family have degree 5 and arithmetic genus 3, and these have a nice interpretation by a BPS number of Y. The proof of the derived equivalence is slightly involved so I explain a similar result in the case where n=3. In this case, we obtain a fully faithful functor from D(X)-> D(Y), where X is a so called the Reye congruence Enriques surface and Y is the 'big resolution' of the Artin-Mumford quartic double solid.
2011年04月18日(月)
16:30-18:00 数理科学研究科棟(駒場) 126号室
川北 真之 氏 (京都大学数理解析研究所)
Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)
川北 真之 氏 (京都大学数理解析研究所)
Ideal-adic semi-continuity problem for minimal log discrepancies (JAPANESE)
[ 講演概要 ]
De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.
De Fernex, Ein and Mustaţă, after Kollár, proved the ideal-adic semi-continuity of log canonicity to obtain Shokurov's ACC conjecture for log canonical thresholds on l.c.i. varieties. I discuss its generalisation to minimal log discrepancies, proposed by Mustaţă.
2011年01月31日(月)
16:40-18:10 数理科学研究科棟(駒場) 126号室
Sukmoon Huh 氏 (KIAS)
Restriction maps to the Coble quartic (ENGLISH)
Sukmoon Huh 氏 (KIAS)
Restriction maps to the Coble quartic (ENGLISH)
[ 講演概要 ]
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.
The Coble sixfold quartic is the moduli space of semi-stable vector bundle of rank 2 on a non-hyperelliptic curve of genus 3 with canonical determinant. Considering the curve as a plane quartic, we investigate the restriction of the semi-stable sheaves over the projective plane to the curve. We suggest a positive side of this trick in the study of the moduli space of vector bundles over curves by showing several examples such as Brill-Noether loci and a few rational subvarieties of the Coble quartic. In a later part of the talk, we introduce the rationality problem of the Coble quartic. If the time permits, we will apply the same idea to the moduli space of bundles over curves of genus 4 to derive some geometric properties of the Brill-Noether loci in the case of genus 4.
2011年01月17日(月)
16:40-18:10 数理科学研究科棟(駒場) 126号室
Dano Kim 氏 (KIAS)
L^2 methods and Skoda division theorems (ENGLISH)
Dano Kim 氏 (KIAS)
L^2 methods and Skoda division theorems (ENGLISH)
[ 講演概要 ]
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.
Extension of Ohsawa-Takegoshi type and division of Skoda type are two important consequences of the L^2 methods of Hormander, Demailly and others. They are analogous to vanishing theorems of Kodaira type and can be viewed as some refinement of the vanishing. The best illustration of their usefulness up to now is Siu’s proof of invariance of plurigenera without general type assumption. In this talk, we will focus on the division theorem / problem and talk about its currently known cases (old and new). One motivation comes from yet another viewpoint on the finite generation of canonical ring.
2010年12月20日(月)
16:40-18:10 数理科学研究科棟(駒場) 126号室
権業 善範 氏 (東大数理)
On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)
権業 善範 氏 (東大数理)
On the minimal model theory from a viewpoint of numerical invariants (JAPANESE)
[ 講演概要 ]
I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)
I will introduce the numerical Kodaira dimension for pseudo-effective divisors after N. Nakayama and explain the minimal model theory of numerical Kodaira dimension zero. I also will talk about the applications. ( partially joint work with B. Lehmann.)
