A Nadel vanishing theorem for metrics with minimal singularities on big line bundles

作者：Matsumura Shin ichi^*

来源：Advances in Mathematics, 2015, 280: 188-207.

DOI：10.1016/j.aim.2015.03.019

• Vanishing theorems
• Singular metrics
• Multiplier ideal sheaves
• The theory of harmonic integrals
• L-2-Methods
• partial derivative-Equation

The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we apply the theory of harmonic integrals and generalize Enoki's proof of Kollar's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.

• 出版日期2015-8-6