Regularity on abelian varieties I

Pareschi, Giuseppe; Popa, Mihnea

doi:10.1090/S0894-0347-02-00414-9

Regularity on abelian varieties I
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by Giuseppe Pareschi and Mihnea Popa

J. Amer. Math. Soc. 16 (2003), 285-302

DOI: https://doi.org/10.1090/S0894-0347-02-00414-9

Published electronically: November 27, 2002

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Abstract:

We introduce the notion of Mukai regularity ($M$-regularity) for coherent sheaves on abelian varieties. The definition is based on the Fourier-Mukai transform, and in a special case depending on the choice of a polarization it parallels and strengthens the usual Castelnuovo-Mumford regularity. Mukai regularity has a large number of applications, ranging from basic properties of linear series on abelian varieties and defining equations for their subvarieties, to higher dimensional type statements and to a study of special classes of vector bundles. Some of these applications are explained here, while others are the subject of upcoming sequels.

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Multiplier Ideals for Algebraic Geometers

Positivity in Algebraic Geometry

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