English

Higher cohomology of the pluricanonical bundle is not deformation invariant

Algebraic Geometry 2008-01-16 v2

Abstract

In this paper, we compute the dimensions of the 1st and 2nd cohomology groups of all the pluricanonical bundles for Hirzebruch surfaces, and the dimensions of the 1st and 2nd cohomology groups of the second pluricanonical bundles for a blow-up of a projective plane along finite many distinct points. Both of them give examples showing that the higher cohomology of the pluricanonical bundle is not deformation invariant.

Keywords

Cite

@article{arxiv.math/0612006,
  title  = {Higher cohomology of the pluricanonical bundle is not deformation invariant},
  author = {Ning Hao and Li Li},
  journal= {arXiv preprint arXiv:math/0612006},
  year   = {2008}
}

Comments

7 pages, correct a typo in the abstract of the first version