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

DOI:
https://doi.org/10.1090/S0894-0347-02-00414-9

Published electronically:
November 27, 2002

MathSciNet review:
1949161

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

**Giuseppe Pareschi**

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

Email:
pareschi@mat.uniroma2.it

**Mihnea Popa**

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

Email:
mpopa@math.harvard.edu

DOI:
https://doi.org/10.1090/S0894-0347-02-00414-9

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