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