Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 14K05, 14K12, 14H40, 14E05

Retrieve articles in all journals with MSC (2000): 14K05, 14K12, 14H40, 14E05


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: http://dx.doi.org/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
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