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Article Dans Une Revue Journal of Algebraic Geometry Année : 2007

Pfaffian lines and vector bundles on Fano threefolds of genus 8

Laurent Manivel

Résumé

Let $X$ be a general complex Fano threefold of genus 8. We prove that the moduli space of rank two semistable sheaves on $X$ with Chern numbers $c_1=1$, $c_2=6$ and $c_3=0$ is isomorphic to the Fano surface $F(X)$ of conics on $X$. This surface is smooth and isomorphic to the Fano surface of lines in the orthogonal to $X$ cubic threefold. Inside $F(X)$, the non-locally free sheaves are parameterized by a smooth curve of genus 26 isomorphic to the base of the family of lines on X.
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Dates et versions

hal-00330597 , version 1 (15-10-2008)

Identifiants

  • HAL Id : hal-00330597 , version 1

Citer

Atanas Iliev, Laurent Manivel. Pfaffian lines and vector bundles on Fano threefolds of genus 8. Journal of Algebraic Geometry, 2007, 16 (3), pp.499-530. ⟨hal-00330597⟩

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