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# Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7

@inproceedings{Iliev2004EllipticCA, title={Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7}, author={Atanas Iliev and Dimitri Markushevich}, year={2004} }

- Published 2004
DOI:10.1515/advg.2004.018

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 Spinð10Þ. It is proven that the moduli space of stable rank-2 vector bundles with Chern classes c1 1⁄4 1, c2 1⁄4 5 on a generic X is isomorphic to the curve of genus 7 obtained by taking an orthogonal linear section of the spinor tenfold. This is an inverse of Mukai’s result on the isomorphism of a non-abelian Brill– Noether locus on a curve of genus 7 to… CONTINUE READING