## Seminar on Geometric Complex Analysis

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

Seminar information archive

### 2011/07/11

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

### 2011/06/20

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

### 2011/01/24

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

### 2010/12/20

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

### 2010/11/08

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

### 2010/10/18

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

### 2010/10/18

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

### 2010/07/12

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Yu KAWAKAMI (Kyushu Univ.)
The value distribution of the Gauss map of wave fronts and its applications (JAPANESE)