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arXiv · 1107.2549

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

Antony Maciocia
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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|.

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Antony Maciocia. 2011-07-18. A Fourier-Mukai Approach to the Enumerative Geometry of Principally Polarized Abelian Surfaces. https://doi.org/10.1002/mana201100182

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