Regularity on abelian varieties I

Pareschi, Giuseppe¹ ; Popa, Mihnea²

¹ Dipartamento di Matematica, Università di Roma, Tor Vergata, V.le della Ricerca Scientifica, I-00133 Roma, Italy
² Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

Journal of the American Mathematical Society, Tome 16 (2003) no. 2, pp. 285-302

Résumé

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.

Détail

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

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