Orateur(s)  Shinichi Matsumura  Kagoshima,

Titre  Versions of injectivity and extension theorems 
Date  03/02/2015 
Horaire  14:00 à 15:00 

Résume  In this talk, I give an injectivity theorem with multiplier ideal sheaves of singular metrics with transcendental singularities. This result can be seen as a generalization of various injectivity and vanishing theorems. The proof is based on a combination of the theory of harmonic integrals and the L²method for the ̄∂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 L²estimates of solutions of the ̄∂equation by using the Cech complex. As applications of this injectivity theorem, I give some extension theorems for holomorphic sections of plurilogcanonical bundle from subvarieties to the ambient space. Moreover, by combining techniques of the minimal model program, we obtain some results for semiampleness related to the abundance conjecture in birational geometry. This talk is based on the preprint in arXiv:1308.2033v2 and a joint work with Y. Gongyo in arXiv:1406.6132v1 
Salle  Barre 1525, 5ème étage, salle 02 
Adresse  Campus Pierre et Marie Curie 