| 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 L²-method 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 L²-estimates 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 pluri-logcanonical bundle from subvarieties to the ambient space. Moreover, by combining techniques of the minimal model program, we obtain some results for semi-ampleness 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 |
