Pfaffian lines and vector bundles on Fano threefolds of genus 8

Abstract

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 c1 = 1, c2 = 6 and c3 = 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. hal-00330597, version 1- 15 Oct 2008 1

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