Abstract
We prove that the moduli space of stable sheaves of rank 2 with the Chern classes c 1 = O Q ( 1 , 1 ) and c 2 = 2 on a smooth quadric Q in P 3 is isomorphic to P 3 . Using this identification, we give a new proof that a Brill–Noether locus, defined as the closure of the stable bundles with at least three linearly independent sections, on a non-hyperelliptic curve of genus 4, is isomorphic to the Donagi–Izadi cubic threefold.
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