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Regularity on abelian varieties I
Author(s):
Giuseppe
Pareschi;
Mihnea
Popa
Journal:
J. Amer. Math. Soc.
16
(2003),
285-302.
MSC (2000):
Primary 14K05;
Secondary 14K12, 14H40, 14E05
Posted:
November 27, 2002
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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:
10.1090/S0894-0347-02-00414-9
PII:
S 0894-0347(02)00414-9
Received by editor(s):
October 22, 2001
Received by editor(s) in revised form:
April 4, 2002
Posted:
November 27, 2002
Additional Notes:
The second author was partially supported by a Clay Mathematics Institute Liftoff Fellowship during the preparation of this paper.
Copyright of article:
Copyright
2002,
American Mathematical Society
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