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- W1681122905 abstract "In the first part of this paper we prove a vanishing criterion for higher direct images of projective families of line bundles on a Cohen-Macaulay variety X. The result involves certain first-order deformations of certain curves on X, and makes essential use of the notion of global co-gaussian maps, a generalization of Wahl's gaussian maps. In the second part we apply the criterion above, combined with Fourier-Mukai transform on abelian varieties, to prove an algebraic version of Green-Lazarsfeld's Generic Vanishing Theorem. In fact we prove a stronger result concerning higher direct images of Poincar'e line bundles, which -- in the compact Kahler setting -- was conjectured by Green and Lazarsfeld and was recently proved, by completely different methods, by Hacon (math.AG/0308198)" @default.
- W1681122905 created "2016-06-24" @default.
- W1681122905 creator A5009206300 @default.
- W1681122905 date "2003-10-02" @default.
- W1681122905 modified "2023-09-27" @default.
- W1681122905 title "Generic vanishing, gaussian maps, and Fourier-Mukai transform" @default.
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