A Fourier-Mukai approach to the enumerative geometry of principally polarized abelian surfaces

Research output: Contribution to journalArticlepeer-review

Abstract

We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface (T,l). Using Fourier-Mukai techniques we associate certain jumping schemes to such sheaves and completely classify such loci. We give examples of applications to the enumerative geometry of T and show that no smooth genus 5 curve on such a surface can contain a g^1_3. We also describe explicitly the singular divisors in the linear system |2l|.
Original languageEnglish
Pages (from-to)1981-1998
Journal Mathematische Nachrichten
Volume285
Issue number16
Early online date2 Jul 2012
DOIs
Publication statusPublished - Nov 2012

Keywords

  • Ideal sheaf
  • Fourier-Mukai
  • divisor
  • abelian surface
  • Hilbert scheme
  • stable sheaf MSC (2010)

Fingerprint

Dive into the research topics of 'A Fourier-Mukai approach to the enumerative geometry of principally polarized abelian surfaces'. Together they form a unique fingerprint.

Cite this