Moduli of sheaves supported on curves of genus two in a quadric surface
arXiv:1612.03566
Abstract
We study the moduli space of stable sheaves of Euler characteristic 1, supported on curves of arithmetic genus 2 contained in a smooth quadric surface. We show that this moduli space is rational. We give a classification of the stable sheaves involving locally free resolutions or extensions. We compute the Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs.
In the second version we correct some errors and we add an important reference