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Article Dans Une Revue Mathematische Zeitschrift Année : 2013

Rank-two stable sheaves with odd determinant on Fano threefolds of genus nine

Résumé

According to Mukai and Iliev, a smooth prime Fano threefold X of genus 9 is associated with a surface ℙ(V), ruled over a smooth plane quartic Γ, and the derived category of Γ embeds into that of X by a theorem of Kuznetsov. We use this setup to study the moduli spaces of rank-2 stable sheaves on X with odd determinant. For each c2 ≥ 7, we prove that a component of their moduli space MX(2, 1, c2) is birational to a Brill-Noether locus of vector bundles with fixed rank and degree on Γ, having enough sections when twisted by V. For c2 = 7, we prove that MX(2, 1, 7) is isomorphic to the blow-up of the Picard variety Pic2(Γ) along the curve parametrizing lines contained in X. © 2012 Springer-Verlag Berlin Heidelberg.

Dates et versions

hal-00866938 , version 1 (27-09-2013)

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M.C. Brambilla, Daniele Faenzi. Rank-two stable sheaves with odd determinant on Fano threefolds of genus nine. Mathematische Zeitschrift, 2013, 275 (1-2), pp.185-210. ⟨10.1007/s00209-012-1131-8⟩. ⟨hal-00866938⟩
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