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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Regularity on abelian varieties I
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by Giuseppe Pareschi and Mihnea Popa
J. Amer. Math. Soc. 16 (2003), 285-302
Published electronically: November 27, 2002


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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Bibliographic Information
  • Giuseppe Pareschi
  • Affiliation: Dipartamento di Matematica, Università di Roma, Tor Vergata, V.le della Ricerca Scientifica, I-00133 Roma, Italy
  • Email:
  • Mihnea Popa
  • Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138
  • MR Author ID: 653676
  • Email:
  • 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:
  • MathSciNet review: 1949161