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Algebraic Geometry Seminar
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
| Date, time & place | Friday 13:30 - 15:00 ハイブリッド開催/117Room #ハイブリッド開催/117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | GONGYO Yoshinori, NAKAMURA Yusuke, TANAKA Hiromu |
2014/02/12
14:00-17:30 Room #122 (Graduate School of Math. Sci. Bldg.)
Shin-ichi Matsumura (Kagoshima University) 14:00-15:30
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)
Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)
Shin-ichi Matsumura (Kagoshima University) 14:00-15:30
An injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities (ENGLISH)
[ Abstract ]
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 (KIAS) 16:00-17:30In 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.
Ohsawa-Takegoshi extension theorem for K\\"ahler manifolds (ENGLISH)
[ Abstract ]
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.
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.
