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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
Published electronically: November 27, 2002
MathSciNet review: 1949161
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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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Additional Information

Giuseppe Pareschi
Affiliation: Dipartamento di Matematica, Università di Roma, Tor Vergata, V.le della Ricerca Scientifica, I-00133 Roma, Italy

Mihnea Popa
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

Received by editor(s): October 22, 2001
Received by editor(s) in revised form: April 4, 2002
Published electronically: November 27, 2002
Additional Notes: The second author was partially supported by a Clay Mathematics Institute Liftoff Fellowship during the preparation of this paper.
Article copyright: © Copyright 2002 American Mathematical Society

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