## 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

### 2019年05月27日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

Gluing construction of K3 surfaces (Japanese)
[ 講演概要 ]
Arnol'd showed the uniqueness of the complex analytic structure of a small neighborhood of an elliptic curve embedded in a surface whose normal bundle satisfies "Diophantine condition" in the Picard variety. By applying this theorem, we construct a K3 surface by holomorphically patching two open complex surfaces obtained as the complements of tubular neighborhoods of anti-canonical curves of blow-ups of the projective planes at general nine points. Our construction has 19 complex dimensional degrees of freedom. For general parameters, the resulting K3 surface is neither Kummer nor projective. By the argument based on the concrete computation of the period map, we also investigate which points in the period domain correspond to K3 surfaces obtained by such construction. (Based on joint work with Takato Uehara)

### 2019年06月17日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
Andrei Pajitnov 氏 (Universite de Nantes)
(English)

### 2019年06月24日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室

(Japanese)

### 2019年07月01日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
Yeping Zhang 氏 (京都大学)
BCOV invariant and birational equivalence (English)
[ 講演概要 ]
Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called BCOV invariant. Now we consider a pair (X,Y), where X is a Kaehler manifold and $Y ¥subseteq X$ is a canonical divisor. In this talk, we extend the BCOV invariant to such pairs. The extended BCOV invariant is well-behaved under birational equivalence. We expect that these considerations may eventually lead to a positive answer to Yoshikawa's conjecture that the BCOV invariant for Calabi-Yau threefold is a birational invariant.

### 2019年07月08日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室