A general vanishing theorem

作者：Laytimi F^*; Nahm W

来源：Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2013, 123(4): 479-490.

DOI：10.1007/s12044-013-0152-5

• Vector bundle
• symmetric product
• exterior product
• Borel-le Potier spectral sequence
• vanishing theorems

Let E be a vector bundle and L be a line bundle over a smooth projective variety X. In this article, we give a condition for the vanishing of Dolbeault cohomology groups of the form H-p,H-q (X, (SE)-E-alpha circle times boolean AND(beta) E circle times L) when S alpha+beta E circle times L is ample. This condition is shown to be invariant under the interchange of p and q. The optimality of this condition is discussed for some parameter values.

• 出版日期2013-11