## 代数幾何学セミナー

開催情報 火曜日　10:30～11:30 or 12:00　数理科学研究科棟(駒場) ハイブリッド開催/002号室 權業 善範・中村 勇哉・田中公

### 2014年02月12日(水)

14:00-17:30   数理科学研究科棟(駒場) 122号室
いつもと曜日・時間が異なります

An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)
[ 講演概要 ]
In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics.
This theorem is a powerful generalization of various injectivity and vanishing theorems.
The proof is based on a combination of the theory of harmonic integrals and the L^2-method for the \\dbar-equation.
To treat transcendental singularities, after regularizing a given singular metric, we study the asymptotic behavior of the harmonic forms with respect to a family of the regularized metrics.
Moreover we obtain L^2-estimates of solutions of the \\dbar-equation, by using the \\check{C}ech complex.
As an application, we obtain a Nadel type vanishing theorem.
Junyan Cao 氏 (KIAS) 16:00-17:30
Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)
[ 講演概要 ]
In this talk, we first prove a version of the Ohsawa-Takegoshi
extension theorem valid for on arbitrary K\\"ahler manifolds, and for
holomorphic line bundles equipped with possibly singular metrics. As an
application, we generalise Berndtsson and Paun 's result about the
pseudo-effectivity of the relative canonical bundles to arbitrary
compact K\\"ahler families.