Vanishing Theorems on Compact Hyper-kähler Manifolds. (16th February 2014) - Yang, Qilin
Abstract : We prove that if B is a k -positive holomorphic line bundle on a compact hyper-kähler manifold M, then H p M, Ω q ⊗ B = 0 for P > n + [ k / 2 ] with q a nonnegative integer. In a special case, k = 0 and q = 0, we recover a vanishing theorem of Verbitsky's with a little stronger assumption.