Antony Maciocia
Published 2011-07-13, updated 2011-07-18Version 2
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|.
Comments: 21 pages with appendix, typos fixed
Journal: Math. Nachr. 285(16) (2012) 1981-1998
Enumerative geometry of the mirror quintic
On K-stability of $\mathbb P^3$ blown up along a smooth genus $2$ curve of degree $5$
Enumerative Geometry of Curvature of Algebraic Hypersurfaces
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