Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
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AbstractWe 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.
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1994 ◽
Vol 1994
(453)
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pp. 193-220
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2003 ◽
Vol 14
(08)
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pp. 837-864
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2014 ◽
Vol 66
(5)
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pp. 961-992
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