Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8

Details Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8 Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8

2005-04-29

arxiv.org/abs/math/0504595v2

Mathematics

Algebraic Geometry

25 pages, LaTeX; to appear in J.Alg.Geom

Scientific paper

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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