Regularity on Abelian varieties II: Basic results on linear series and defining equations

Giuseppe Pareschi*, Mihnea Popa

*Corresponding author for this work

Research output: Contribution to journalArticle

17 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)167-193
Number of pages27
JournalJournal of Algebraic Geometry
Volume13
Issue number1
DOIs
StatePublished - Jan 2004

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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