Vanishing Theorems on Compact Hyperkähler Manifolds

2010/10/13 by Yang, Qi-Lin
#14F17 #32L10 #53C43 #58E20 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1010.2555

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⊗ B)=0 for p>n+[(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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