A derived category approach to generic vanishing

2003/08/20 by Christopher D. Hacon, Hacon, Christopher D. · 5 citations
Mathematics · #14F17 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14F17

paper · pdf · doi:10.48550/arxiv.math/0308198

11 pages, comments welcome

arxiv created 2003/08/20 · arxiv updated 2009/12/01

Abstract

We prove a Generic Vanishing Theorem for coherent sheaves on an abelian variety over an algebraically closed field k. When k=\CC this implies a conjecture of Green and Lazarsfeld.

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• Singularities of base loci on abelian varieties
• Hyperbolicity of adjoint linear series on varieties with positive tangent bundle
• On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension
• Generic vanishing theory in positive characteristic
• A valuative approach to the anticanonical minimal model program

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