## Seminar on Geometric Complex Analysis

Seminar information archive ～02/07｜Next seminar｜Future seminars 02/08～

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, Ryosuke Nomura |

**Seminar information archive**

### 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)

### 2010/07/05

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

Expression of restricted volumes with current integration (JAPANESE)

**Shin-ichi MATSUMURA**(Univ. of Tokyo)Expression of restricted volumes with current integration (JAPANESE)

### 2010/06/28

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

Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

**Kengo HIRACHI**(Univ. of Tokyo)Total Q-curvature vanishes on integrable CR manifolds (ENGLISH)

### 2010/06/21

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

A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

**Sachiko HAMANO**(Fukushima Univ)A remark on C^1 subharmonicity of the harmonic spans for discontinuously moving Riemann surfaces (JAPANESE)

### 2010/06/14

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

Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

**Kazuko MATSUMOTO**(Osaka Prefecture University)Degeneracy condition for Levi form of distance to Levi flat real hypersurfaces in C^n (JAPANESE)

### 2010/06/07

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

Restricted Bergman kernel asymptotics (JAPANESE)

**Tomoyuki HISAMOTO**(Univ. of Tokyo)Restricted Bergman kernel asymptotics (JAPANESE)

### 2010/05/31

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

Singularities and analytic torsion (JAPANESE)

**Ken-ichi YOSHIKAWA**(Kyoto Univ.)Singularities and analytic torsion (JAPANESE)

### 2010/05/17

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

On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

**Masaharu TANABE**(Tokyo Inst. Tech.)On the norm defined on the holomorphic maps of compact Riemann surfaces (JAPANESE)

### 2010/05/10

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

Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

**Yoshihiko MATSUMOTO**(Univ. of Tokyo)Asymptotics of ACH-Einstein metrics, and an invariant tensor of partially-integrable almost CR manifolds (JAPANESE)

[ Abstract ]

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

To investigate strictly pseudoconvex partially-integrable almost CR manifolds as boundaries at infinity of noncompact complete Riemannian spaces, we study the Einstein equation for ACH metrics. At the jet level (of a certain order that depends only on the dimension) along the boundary, a solution uniquely exists up to the action of boundary-preserving diffeomorphisms. If we further consider higher-order solutions, without logarithmic singularities, in general we encounter an obstruction for construction, which is a local invariant tensor of the boundary. Some properties of that invariant tensor are also mentioned.

### 2010/04/26

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

Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

**Yoshihiro AIHARA**(Fukushima Univ.)Deficiencies of holomorphic curves in projective algebraic varieties (JAPANESE)

### 2010/04/19

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

Loewner's theory on complex manifolds (ENGLISH)

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**Filippo Bracci**(Universita di Roma, ``Tor Vergata'')Loewner's theory on complex manifolds (ENGLISH)

[ Abstract ]

Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

[ Reference URL ]Loewner's theory, introduced by Ch. Loewner in 1923 and developed later by Pommerenke, Kufarev, Schramm and others, has been proved to be a very powerful tool in studying extremal problems. In this talk we are going to describe a unified and general view of the deterministic Loewner theory both on the unit disc and on Kobayashi hyperbolic manifolds.

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/04/12

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

Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

**千葉 優作**(東大数理)Degeneracy of holomorphic curves into the complements of hypersurfaces in a complex projective space

[ Reference URL ]

http://info.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

### 2010/02/01

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

Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

**大沢健夫**(名古屋大学多元数理科学研究科)Connectedness of Levi nonflat pseudoconvex hypersurfaces in Kaehler manifolds

### 2010/01/25

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

Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

**Colin Guillarmou**(Ecole Normale Superieure)Eta invariant and Selberg Zeta function of odd type over convex co-compact hyperbolic manifolds

### 2010/01/18

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

スプライス商特異点について

**奥間智弘**(山形大学地域教育文化学部)スプライス商特異点について

### 2009/12/17

16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)

Hyperbolicity of cycle spaces and automorphism groups of flag domains

**Alan Huckleberry**(Ruhr-Universität Bochum)Hyperbolicity of cycle spaces and automorphism groups of flag domains

### 2009/11/30

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

Equidistribution and Nevanlinna theory

**奥山裕介**(京都工芸繊維大学)Equidistribution and Nevanlinna theory

### 2009/11/16

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

Weighted Green functions of polynomial skew products on C^2

**上野康平**(京都大学大学院理学研究科)Weighted Green functions of polynomial skew products on C^2

### 2009/10/26

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

On Vojta's conjecture in the split function field case

**Pietro Corvaja**(Università di Udine)On Vojta's conjecture in the split function field case