Regularity on abelian varieties I
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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.
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
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