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

Antony Maciocia

doi:10.1002/mana.201100182

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

Antony Maciocia

School of Mathematics

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1981-1998
Journal	Mathematical News
Volume	285
Issue number	16
Early online date	2 Jul 2012
DOIs	https://doi.org/10.1002/mana.201100182
Publication status	Published - Nov 2012

Keywords / Materials (for Non-textual outputs)

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

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10.1002/mana.201100182

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AB - 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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KW - Fourier-Mukai

KW - divisor

KW - abelian surface

KW - Hilbert scheme

KW - stable sheaf MSC (2010)

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EP - 1998

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JF - Mathematical News

IS - 16

ER -

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

Abstract

Keywords / Materials (for Non-textual outputs)

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