Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces

研究成果: Article査読

9 被引用数 (Scopus)

抄録

In this paper, we study relations between positivity of the curvature and the asymptotic behavior of the higher cohomology group for tensor powers of a holomorphic line bundle. The Andreotti-Grauert vanishing theorem asserts that partial positivity of the curvature implies asymptotic vanishing of certain higher cohomology groups. We investigate the converse implication of this theorem under various situations. For example, we consider the case where a line bundle is semi-ample or big. Moreover, we show the converse implication holds on a projective surface without any assumptions on a line bundle.

本文言語English
ページ(範囲)2199-2221
ページ数23
ジャーナルAnnales de l'Institut Fourier
63
6
DOI
出版ステータスPublished - 2013 1 1
外部発表はい

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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