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

  • Mario Maican EMAIL logo
From the journal Advances in Geometry

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 α-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.

MSC 2010: Primary 14D20; 14D22
  1. Communicated by: R. Cavalieri

Acknowledgement

The author would like to thank Jean-Marc Drézet for several helpful discussions.

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Received: 2018-05-19
Revised: 2018-08-17
Published Online: 2020-10-08
Published in Print: 2020-10-27

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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