Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



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), 167-193
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 Fourier-Mukai 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, I-00133 Roma, Italy

Mihnea Popa
Affiliation: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, Massachusetts 02138

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.