Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8

Atanas Iliev; Laurent Manivel

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Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8

Atanas Iliev·Laurent Manivel

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Abstract

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. 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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BibTeX RIS

Atanas Iliev, Laurent Manivel. 2005-12-09. Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8. https://arxiv.org/abs/math/0504595

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