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- W1751569401 abstract "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." @default.
- W1751569401 created "2016-06-24" @default.
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- W1751569401 date "2011-04-28" @default.
- W1751569401 modified "2023-10-16" @default.
- W1751569401 title "Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces" @default.
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- W1751569401 doi "https://doi.org/10.48550/arxiv.1104.5313" @default.
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