ASYMPTOTIC COHOMOLOGY VANISHING AND A CONVERSE TO THE ANDREOTTI-GRAUERT THEOREM ON SURFACES

Shin-ichi MATSUMURA

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ASYMPTOTIC COHOMOLOGY VANISHING AND A CONVERSE TO THE ANDREOTTI-GRAUERT THEOREM ON SURFACES

机译：ASYMPTOTIC COHOMOLOGY VANISHING AND A CONVERSE TO THE ANDREOTTI-GRAUERT THEOREM ON SURFACES

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摘要

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.

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来源
《Annales de l'Institut Fourier》 |2013年第6期|2199-2221|共23页
作者
Shin-ichi MATSUMURA;
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作者单位

Department of Mathematics and Computer Science, Kagoshima University, 1-21-35 Koorimoto, Kagoshima 890-0065, Japan.;

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正文语种英语
中图分类自然科学总论;
关键词
Asymptotic cohomology groups; partial cohomology vanishing; q-positivity; hermitian metrics; Chern curvatures.;

ASYMPTOTIC COHOMOLOGY VANISHING AND A CONVERSE TO THE ANDREOTTI-GRAUERT THEOREM ON SURFACES

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