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

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dc.creatorIliev, A.
dc.creatorMarkushevich, D.
dc.date2002-09-09
dc.date.accessioned2026-07-07T04:50:42Z
dc.date.available2026-07-07T04:50:42Z
dc.descriptionAccording 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). It is proven that the moduli space of stable rank-2 vector bundles with Chern classes c_1=1,c_2=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 a Fano threefold of genus 7. An explicit geometric construction of both isomorphisms and a similar result for K3 surfaces of genus 7 are given.
dc.description37 pages
dc.identifierhttps://arxiv.org/abs/math/0209094
dc.identifierhttp://arxiv.org/abs/math/0209094
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64889
dc.subjectAlgebraic Geometry
dc.subject14J30
dc.titleElliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7
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