## 複素解析幾何セミナー

開催情報 月曜日　10:30～12:00　数理科学研究科棟(駒場) 128号室 平地 健吾, 高山 茂晴, 野村 亮介

### 2017年05月08日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

Semipositivity theorems for a variation of Hodge structure
[ 講演概要 ]
I will talk about my recent joint work with Osamu Fujino. The main purpose of our joint work is to generalize the Fujita-Zukcer-Kawamata semipositivity theorem from the analytic viewpoint. In this talk, I would like to illustrate the relation between the two objects, the asymptotic behavior of a variation of Hodge structure and good properties of the induced singular hermitian metric on an invertible subbundle of the Hodge bundle.

### 2017年05月15日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

On the moduli spaces of the tangent cones at infinity of some hyper-Kähler manifolds
[ 講演概要 ]
For a metric space $(X,d)$, the Gromov-Hausdorff limit of $(X, a_n d)$ as $a_n \rightarrow 0$ is called the tangent cone at infinity of $(X,d)$. Although the tangent cone at infinity always exists if $(X,d)$ comes from a complete Riemannian metric with nonnegative Ricci curvature, the uniqueness does not hold in general. Colding and Minicozzi showed the uniqueness under the assumption that $(X,d)$ is a Ricci-flat manifold satisfying some additional conditions.
In this talk, I will explain a example of noncompact complete hyper-Kähler manifold who has several tangent cones at infinity, and determine the moduli space of them.

### 2017年05月22日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

Complex K3 surfaces containing Levi-flat hypersurfaces
[ 講演概要 ]
We show the existence of a complex K3 surface $X$ which is not a Kummer surface and has a one-parameter family of Levi-flat hypersurfaces in which all the leaves are dense. We construct such $X$ by patching two open complex surfaces obtained as the complements of tubular neighborhoods of elliptic curves embedded in blow-ups of the projective planes at general nine points.

### 2017年05月29日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

LCK structures on compact solvmanifolds
[ 講演概要 ]
A locally conformal Kähler (in short LCK) manifold is said to be Vaisman if Lee form is parallel with respect to Levi-Civita connection. In this talk, we prove that a Vaisman structure on a compact solvmanifolds depends only on the form of the fundamental 2-form, and it do not depends on a complex structure. As an application, we give the structure theorem for Vaisman (completely solvable) solvmanifolds and LCK nilmanifolds. Moreover, we show the existence of LCK solvmanifolds without Vaisman structures.

### 2017年06月12日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2017年06月19日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2017年06月26日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA

### 2017年07月03日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

TBA
[ 講演概要 ]
TBA