Vanishing theorems on toric varieties
Copyright policy )Vanishing theorems on toric varieties
We use Cox's description for sheaves on toric varieties and results about the local cohomology with respect to monomial ideals to give a characteristic free approach to vanishing results on arbitrary toric varieties. As an application, we give a proof of a strong form of Fujita's conjecture in the case of toric varieties. We also prove that every sheaf on a toric variety corresponds to a module over the homogeneous coordinate ring, generalizing Cox's result for the simplicial case.
21 pages. Revised version, to appear in Tohoku Mathematical Journal
- Clay Mathematics Institute United States
14F17 (Secondary), 14M25 (Primary); 14F17 (Secondary), Sheaves, derived categories of sheaves, etc., Toric varieties, vanishing theorems, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Algebraic Geometry, homogeneous coordinate ring, Fujita's Conjecture, FOS: Mathematics, 14F17, Toric varieties, Newton polyhedra, Okounkov bodies, 14M25 (Primary), 14M25, Algebraic Geometry (math.AG), Vanishing theorems in algebraic geometry
14F17 (Secondary), 14M25 (Primary); 14F17 (Secondary), Sheaves, derived categories of sheaves, etc., Toric varieties, vanishing theorems, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), Mathematics - Algebraic Geometry, homogeneous coordinate ring, Fujita's Conjecture, FOS: Mathematics, 14F17, Toric varieties, Newton polyhedra, Okounkov bodies, 14M25 (Primary), 14M25, Algebraic Geometry (math.AG), Vanishing theorems in algebraic geometry
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