English

Vanishing theorems and the multigraded regularity of nonsingular subvarieties

Algebraic Geometry 2012-08-03 v1

Abstract

Given scheme-theoretic equations for a nonsingular subvariety, we prove that the higher cohomology groups for suitable twists of the corresponding ideal sheaf vanish. From this result, we obtain linear bounds on the multigraded Castelnuovo-Mumford regularity of a nonsingular subvariety, and new criteria for the embeddings by adjoint line bundles to be projectively normal. A special case of our work recovers the vanishing theorem of Bertram, Ein, and Lazarsfeld.

Keywords

Cite

@article{arxiv.1208.0484,
  title  = {Vanishing theorems and the multigraded regularity of nonsingular subvarieties},
  author = {Victor Lozovanu and Gregory G. Smith},
  journal= {arXiv preprint arXiv:1208.0484},
  year   = {2012}
}

Comments

15 pages, 1 figure