Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vanishing Theorems on Compact Hyperk\"ahler Manifolds   We prove that if $B$ is a $k$-positive holomorphic line bundle on a compact
hyperk\"ahler 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.

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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph