A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces

Details A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces

2011-07-13

arxiv.org/abs/1107.2549v2

Mathematics

Algebraic Geometry

21 pages with appendix, typos fixed

Scientific paper

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|.

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