Vanishing Theorems on Compact Hyperkähler Manifolds

Abstract

We prove that if $B$ is a $k$-positive holomorphic line bundle on a compact hyperkähler manifold $M,$ then $H^p(M,{\Omega }^q\otimes B)=0$ 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.

24pages