Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8
Algebraic Geometry
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0504595,
title = {Pfaffian Lines and Vector Bundles on Fano Threefolds of Genus 8},
author = {Atanas Iliev and Laurent Manivel},
journal= {arXiv preprint arXiv:math/0504595},
year = {2007}
}
Comments
25 pages, LaTeX; to appear in J.Alg.Geom