## Regularity on abelian varieties I

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- by Giuseppe Pareschi and Mihnea Popa
- J. Amer. Math. Soc.
**16**(2003), 285-302 - DOI: https://doi.org/10.1090/S0894-0347-02-00414-9
- Published electronically: November 27, 2002
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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.## References

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[PP2]pp2 G. Pareschi and M. Popa, in preparation.
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## Bibliographic 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
- MR Author ID: 653676
- Email: mpopa@math.harvard.edu
- 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.
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1949161