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Article Dans Une Revue International Journal of Mathematics Année : 2014

Vector bundles on Fano threefolds of genus 7 and Brill-Noether loci

Résumé

Let X be a smooth prime Fano threefold of genus 7 and let Γ be its homologically projectively dual curve. We prove that, for d ≥ 6, an irreducible component of the moduli scheme MX(2, 1, d) of rank-2 stable sheaves on X with c1 = 1, c2 = d is birational to a generically smooth (2d - 9)-dimensional component of the Brill-Noether variety W 2d-11/d-5, 5 d-24 of stable vector bundles on Γ of rank d - 5 and degree 5d-24 with at least 2d - 10 independent global sections. The space M X(2, 1, 6) is proved to be isomorphic to W1/1, 6 and to be a smooth irreducible threefold if X is general enough.© 2014 World Scientific Publishing Company.

Dates et versions

hal-00993812 , version 1 (20-05-2014)

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M.C. Brambilla, Daniele Faenzi. Vector bundles on Fano threefolds of genus 7 and Brill-Noether loci. International Journal of Mathematics, 2014, 25 (3), ⟨10.1142/S0129167X14500232⟩. ⟨hal-00993812⟩
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