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arXiv · 1704.00810

Moduli of stable sheaves supported on curves of genus three contained in a quadric surface

Mario Maican
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Abstract

We study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of alpha-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.

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Mario Maican. 2017-04-03. Moduli of stable sheaves supported on curves of genus three contained in a quadric surface. https://arxiv.org/abs/1704.00810

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