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arXiv · 1211.6283

A vanishing theorem

Nahm Werner·Laytimi Fatima
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Abstract

Let $E$ be a vector bundle and $L$ be a line bundle over a smooth projective variety $X$. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form $H^{p,q}(X,\SSS^{\alpha}E\otimes \wedge^{\beta} E\otimes L)$ when $S^{\alpha+\beta}E \otimes L$ is ample. This condition is shown to be invariant under the interchange of $p$ and $q$. The optimality of this condition is discussed for some parameter values.

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Nahm Werner, Laytimi Fatima. 2012-11-27. A vanishing theorem. https://arxiv.org/abs/1211.6283

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