## Seminar on Geometric Complex Analysis

Seminar information archive ～05/21｜Next seminar｜Future seminars 05/22～

Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
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Organizer(s) | Kengo Hirachi, Shigeharu Takayama |

**Seminar information archive**

### 2011/07/11

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Kobayashi hyperbolic imbeddings into toric varieties (JAPANESE)

**Yusaku Chiba**(University of Tokyo)Kobayashi hyperbolic imbeddings into toric varieties (JAPANESE)

### 2011/07/04

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Toward a Hirzebruch-Riemann-Roch formula in CR geometry (ENGLISH)

**Raphael Ponge**(University of Tokyo)Toward a Hirzebruch-Riemann-Roch formula in CR geometry (ENGLISH)

### 2011/06/27

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)

**Kyoji Saito**(IPMU, University of Tokyo)Vanishing cycles for the entire functions of type $A_{1/2\infty}$ and $D_{1/2\infty}$ (JAPANESE)

[ Abstract ]

We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.

We introduce two elementary transcendental functions $f_{A_{1/2\infty}}$ and $f_{D_{1/2\infty}}$ of two variables. They have countably infinitely many critical points. Then, the vanishing cycles associated with the critical points form Dynkin diagrams of type $A_{1/2\infty}$ and $D_{1/2\infty}$. We calculate the spectral decomposition of the monodromy transformation by embedding the lattice of vanishing cycles into a Hilbert space. All these stories are connected with a new understanding of KP and KdV integral hierarchy. But the relationship is not yet clear.

### 2011/06/20

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Domains which satisfy the Oka-Grauert principle in a Stein space (JAPANESE)

**Makoto Abe**(Hiroshima University)Domains which satisfy the Oka-Grauert principle in a Stein space (JAPANESE)

### 2011/06/13

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the complement of effective divisors with semipositive normal bundle (JAPANESE)

**Takeo Ohsawa**(Nagoya Univeristy)On the complement of effective divisors with semipositive normal bundle (JAPANESE)

### 2011/06/06

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)

**Tomoko Shinohara**(Tokyo Metropolitan College of Industrial Technology)An invariant surface of a fixed indeterminate point for rational mappings (JAPANESE)

### 2011/05/30

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)

**Atusi Yamamori**(Meiji University)On the Forelli-Rudin construction and explicit formulas of the Bergman kernels (JAPANESE)

### 2011/05/16

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Linearity of order isomorphisms of regular convex cones (JAPANESE)

**Chifune Kai**(Kanazawa Univeristy)Linearity of order isomorphisms of regular convex cones (JAPANESE)

### 2011/05/09

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Order of meromorphic maps and rationality of the image space (JAPANESE)

**Junjiro Noguchi**(University of Tokyo)Order of meromorphic maps and rationality of the image space (JAPANESE)

### 2011/04/25

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

On the classification of CR mappings between generalized pseudoellipsoids (JAPANESE)

**Atsushi Hayashimoto**(Nagano National College of Technology)On the classification of CR mappings between generalized pseudoellipsoids (JAPANESE)

### 2011/04/18

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

**Shinichi Matsumura**(University of Tokyo)Asymptotic cohomology vanishing and a converse of the Andreotti-Grauert theorem on surface (JAPANESE)

### 2011/04/11

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Algebraic analysis of resolvents and an exact algorithm for computing Spectral decomposition matrices (JAPANESE)

**Shinichi Tajima**(University of Tsukuba)Algebraic analysis of resolvents and an exact algorithm for computing Spectral decomposition matrices (JAPANESE)

### 2011/01/31

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Varieties with ample cotangent bundle and hyperbolicity (ENGLISH)

**Damian Brotbek**(Rennes Univ.)Varieties with ample cotangent bundle and hyperbolicity (ENGLISH)

[ Abstract ]

Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.

Varieties with ample cotangent bundle satisfy many interesting properties and are supposed to be abundant, however relatively few concrete examples are known. In this talk we will construct such examples as complete intersection surfaces in projective space, and explain how this problem is related to the study of hyperbolicity properties for hypersurfaces.

### 2011/01/24

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Toward a complex analytic 3-dimensional Kleinian group theory (JAPANESE)

**Masahide Kato**(Sophia Univ.)Toward a complex analytic 3-dimensional Kleinian group theory (JAPANESE)

### 2011/01/17

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)

**Toshihiro Nose**(Kyushu Univ.)Asymptotics of the Bergman function for semipositive holomorphic line bundles (JAPANESE)

[ Abstract ]

In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

In this talk, an asymptotic expansion of the Bergman function at a degenerate point is given for high powers of semipositive holomorphic line bundles on compact Kahler manifolds, whose Hermitian metric has some kind of quasihomogeneous properties. In the sence of pointwise asymptotics, This expansion is a generalization of the expansion of Tian-Zelditch-Catlin-Lu in the positive line bundle case.

### 2010/12/20

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Pseudoconvex domains in Hopf surfaces (JAPANESE)

**Hiroshi Yamaguchi**(Shiga Univ*)Pseudoconvex domains in Hopf surfaces (JAPANESE)

### 2010/12/13

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

An equality estimate for the second main theorem (JAPANESE)

**Katsutoshi Yamanoi**(Tokyo Institute of Technology)An equality estimate for the second main theorem (JAPANESE)

### 2010/12/06

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Chow semistability of polarized toric manifolds (JAPANESE)

**Hajime Ono**(Tokyo Univ of Science)Chow semistability of polarized toric manifolds (JAPANESE)

### 2010/11/15

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Excess intersections and residues in improper dimension (JAPANESE)

**Tatsuo Suwa**(Hokkaido Univ*)Excess intersections and residues in improper dimension (JAPANESE)

[ Abstract ]

This talk concerns localization of characteristic classes and associated residues, in the context of intersection theory and residue theory of singular holomorphic foliations. The localization comes from the vanishing of certain characteristic forms, usually caused by the existence of some geometric object, away from the "singular set" of the object. This gives rise to residues in the homology of the singular set and residue theorems relating local and global invariants. In the generic situation, i.e., if the dimension of the singular set is "proper", we have a reasonable understanding of the residues. We indicate how to cope with the problem when the dimension is "excessive" (partly a joint work with F. Bracci).

This talk concerns localization of characteristic classes and associated residues, in the context of intersection theory and residue theory of singular holomorphic foliations. The localization comes from the vanishing of certain characteristic forms, usually caused by the existence of some geometric object, away from the "singular set" of the object. This gives rise to residues in the homology of the singular set and residue theorems relating local and global invariants. In the generic situation, i.e., if the dimension of the singular set is "proper", we have a reasonable understanding of the residues. We indicate how to cope with the problem when the dimension is "excessive" (partly a joint work with F. Bracci).

### 2010/11/08

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Variation of canonical measures under Kaehler deformations (JAPANESE)

**Hajime Tsuji**(Sophia Univ)Variation of canonical measures under Kaehler deformations (JAPANESE)

### 2010/10/26

13:00-14:30 Room #123 (Graduate School of Math. Sci. Bldg.)

Limits of Moishezon Manifolds under Holomorphic Deformations (ENGLISH)

**Dan Popovici**(Toulouse)Limits of Moishezon Manifolds under Holomorphic Deformations (ENGLISH)

[ Abstract ]

We prove that if all the fibres, except one, of a holomorphic family of compact complex manifolds are supposed to be Moishezon (i.e. bimeromorphic to projective manifolds), then the remaining (limit) fibre is again Moishezon. The two ingredients of the proof are the relative Barlet space of divisors contained in the fibres for which we show properness over the base of the family and the "strongly Gauduchon" (sG) metrics that we have introduced for the purpose of controlling volumes of cycles. These new metrics enjoy stability properties under both deformations and modifications and play a crucial role in obtaining a uniform control on volumes of relative divisors that prove the above-mentioned properness.

We prove that if all the fibres, except one, of a holomorphic family of compact complex manifolds are supposed to be Moishezon (i.e. bimeromorphic to projective manifolds), then the remaining (limit) fibre is again Moishezon. The two ingredients of the proof are the relative Barlet space of divisors contained in the fibres for which we show properness over the base of the family and the "strongly Gauduchon" (sG) metrics that we have introduced for the purpose of controlling volumes of cycles. These new metrics enjoy stability properties under both deformations and modifications and play a crucial role in obtaining a uniform control on volumes of relative divisors that prove the above-mentioned properness.

### 2010/10/18

10:30-11:30 Room #128 (Graduate School of Math. Sci. Bldg.)

Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)

**Sergey Ivashkovitch**(Univ. de Lille)Limiting behavior of minimal trajectories of parabolic vector fields on the complex projective plane. (ENGLISH)

[ Abstract ]

The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.

The classical Poincare-Bendixson theory describes the way a trajectory of a vector field on the real plane behaves when accumulating to the singular locus of the vector field. We shall describe, in the first approximation, the way a minimal trajectory of a parabolic complex polynomial vector field (or, a holomorphic foliation) on the complex projective plane approaches the singular locus. In particular we shall prove that if a holomorphic foliation has an exceptional minimal set then its nef model is necessarily hyperbolic.

### 2010/10/18

13:00-14:00 Room #128 (Graduate School of Math. Sci. Bldg.)

Degenerate complex Monge-Ampere equations (ENGLISH)

**Philippe Eyssidieux**(Institut Fourier, Grenoble)Degenerate complex Monge-Ampere equations (ENGLISH)

### 2010/10/04

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)

**Hideyuki ISHI**(Nagoya Univ)The canonical coordinates associated to homogeneous Kaehler metrics on a homogeneous bounded domain (JAPANESE)

[ Abstract ]

For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.

Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

For a real analytic Kaehler manifold, one can define a canonical coordinate, called the Bochner coordinate, around each point. In this talk, we show that the canonical cooredinate is globally defined for a bounded homogeneous domain with a homogeneous Kaehler manifold, which is not necessarily the Bergman metric.

Then we obtain a standard realization of the homogeneous domain associated to the homogeneous metric.

### 2010/07/12

10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)

The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)

**Yu KAWAKAMI**(Kyushu Univ.)The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)