Regularity on abelian varieties II: Basic results on linear series and defining equations
Authors:
Giuseppe Pareschi and Mihnea Popa
Journal:
J. Algebraic Geom. 13 (2004), 167193
DOI:
https://doi.org/10.1090/S105639110300345X
Published electronically:
August 21, 2003
MathSciNet review:
2008719
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Abstract  References  Additional Information
Abstract: We apply the theory of $M$regularity developed by the authors [Regularity on abelian varieties, I, J. Amer. Math. Soc. 16 (2003), 285–302] to the study of linear series given by multiples of ample line bundles on abelian varieties. We define an invariant of a line bundle, called $M$regularity index, which governs the higher order properties and (partly conjecturally) the defining equations of such embeddings. We prove a general result on the behavior of the defining equations and higher syzygies in embeddings given by multiples of ample bundles whose base locus has no fixed components, extending a conjecture of Lazarsfeld [proved in Syzygies of abelian varieties, J. Amer. Math. Soc. 13 (2000), 651–664]. This approach also unifies essentially all the previously known results in this area, and is based on FourierMukai techniques rather than representations of theta groups.

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Additional Information
Giuseppe Pareschi
Affiliation:
Dipartamento di Matematica, Università di Roma, Tor Vergata, V.le della Ricerca Scientifica, I00133 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 21, 2001
Published electronically:
August 21, 2003
Additional Notes:
The second author was partially supported by a Clay Mathematics Institute Liftoff Fellowship during the preparation of this paper.