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Parametrization of Sing(Theta) for a Fano 3-fold of genus 7 by moduli of vector bundles

Atanas Iliev·Dimitri Markushevich
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Abstract

According to Mukai, any prime Fano threefold X of genus 7 is a linear section of the spinor tenfold in the projectivized half-spinor space of Spin(10). The orthogonal linear section of the spinor tenfold is a canonical genus-7 curve G, and the intermediate Jacobian J(X) is isomorphic to the Jacobian of G. It is proven that, for a generic X, the Abel-Jacobi map of the family of elliptic sextics on X factors through the moduli space of rank-2 vector bundles with c_1=-K_X and deg c_2=6 and that the latter is birational to the singular locus of the theta divisor of J(X).

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Atanas Iliev, Dimitri Markushevich. 2007-03-06. Parametrization of Sing(Theta) for a Fano 3-fold of genus 7 by moduli of vector bundles. https://arxiv.org/abs/math/0403122

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