Giuseppe Pareschi, Mihnea Popa
Published 2001-09-30, updated 2003-06-05Version 2
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 strenghtens 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 make the subject of upcoming papers.
Comments: 18 pages; final version, with substantial changes in the order of presentation in Section 2, and other minor expository changes, as suggested by the referee
Journal: J. Amer. Math. Soc. 16 (2003), no.2, 285-302
Regularity on abelian varieties II: basic results on linear series and defining equations
Regularity on abelian varieties III: relationship with Generic Vanishing and applications
An inductive approach to the Hodge conjecture for abelian varieties
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