Regularity on abelian varieties I

Pareschi, Giuseppe; Popa, Mihnea

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

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Regularity on abelian varieties I

Authors: Giuseppe Pareschi and Mihnea Popa
Journal: J. Amer. Math. Soc. 16 (2003), 285-302
MSC (2000): Primary 14K05; Secondary 14K12, 14H40, 14E05
Posted: November 27, 2002
MathSciNet review: 1949161
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Abstract: We introduce the notion of Mukai regularity (-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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