Vanishing theorems and the multigraded regularity of nonsingular subvarieties

2012/08/02 by Victor Lozovanu, Gregory G. Smith, Lozovanu, Victor +1 · 1 citation
Computer Science · Mathematics · #14F17 #14M10 #14Q20 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1208.0484

openalex publication_date 2012/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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