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arXiv · 1010.2555

Vanishing Theorems on Compact Hyperkähler Manifolds

Qi-Lin Yang
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Abstract

We prove that if $B$ is a $k$-positive holomorphic line bundle on a compact hyperkähler manifold $M,$ then $H^p (M,Ω^q\otimes B)=0$ for $p>n+[\frac{k}{2}]$ and any nonnegative integer $q.$ In a special case $k=0$ and $q=0$ we recover a vanishing theorem of Verbitsky's with a little stronger assumption.

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Qi-Lin Yang. 2010-10-13. Vanishing Theorems on Compact Hyperkähler Manifolds. https://arxiv.org/abs/1010.2555

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