Vanishing theorems and the multigraded regularity of nonsingular subvarieties

Victor Lozovanu; Gregory G. Smith

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arXiv · 1208.0484

Vanishing theorems and the multigraded regularity of nonsingular subvarieties

Victor Lozovanu·Gregory G. Smith

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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.

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Victor Lozovanu, Gregory G. Smith. 2012-08-02. Vanishing theorems and the multigraded regularity of nonsingular subvarieties. https://arxiv.org/abs/1208.0484

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