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

Complex Variables 2015-11-16 v3 Algebraic Geometry Differential Geometry

Abstract

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 Koll'ar's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.

Keywords

Cite

@article{arxiv.1306.2497,
  title  = {A Nadel vanishing theorem for metrics with minimal singularities on big line bundles},
  author = {Shin-ichi Matsumura},
  journal= {arXiv preprint arXiv:1306.2497},
  year   = {2015}
}

Comments

18pages, to appear in Adv. Math. 280 (2015), 188--207, v3: completely revised version