A Fourier‐Mukai approach to the enumerative geometry of principally polarized abelian surfaces |
| |
| Authors: | Antony Maciocia |
| |
| Institution: | Department of Mathematics and Statistics, The University of Edinburgh, The King's Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK. Phone: +44 131650 5994, Fax: +44 131650 6553 |
| |
| Abstract: | We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )We study twisted ideal sheaves of small length on an irreducible principally polarized abelian surface $({\mathbb T},\ell )$. 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 ${\mathbb T}$ 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 |2?|. |
| |
| Keywords: | Ideal sheaf Fourier‐Mukai divisor abelian surface Hilbert scheme stable sheaf MSC (2010) 14F05 14N10 14N20 14J60 14D20 14K30 14C20 |
|
|
