Displaying similar documents to “Cohomology and splitting of Hermitian-Einstein vector bundles.”

Positivity on subvarieties and vanishing of higher cohomology

Alex Küronya (2013)

Annales de l’institut Fourier

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We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.

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

Shin-ichi Matsumura (2013)

Annales de l’institut Fourier

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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....

Vanishing theorems on cohomology associated to hermitian symmetric spaces

Shingo Murakami (1987)

Annales de l'institut Fourier

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We consider the cohomoly groups of compact locally Hermitian symmetric spaces with coefficients in the sheaf of germs of holomorphic sections of those vector bundles over the spaces which are defined by canonical automorphic factors. We give a quick survey of the research on these cohomology groups, and then discuss vanishing theorems of the cohomology groups.