Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Pfaffian lines and vector bundles on Fano threefolds of genus $ 8$


Authors: Atanas Iliev and Laurent Manivel
Journal: J. Algebraic Geom. 16 (2007), 499-530
DOI: https://doi.org/10.1090/S1056-3911-07-00440-7
Published electronically: February 6, 2007
MathSciNet review: 2306278
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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$. This surface is smooth and isomorphic to the Fano surface of lines in the orthogonal to $ X$ cubic threefold. Inside $ F(X)$, the nonlocally free sheaves are parameterized by a smooth curve of genus $ 26$ isomorphic to the base of the family of lines on $ \textrm{X}$.


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Atanas Iliev
Affiliation: Institute of Mathematics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 8, 1113 Sofia, Bulgaria
Email: ailiev@math.bas.bg

Laurent Manivel
Affiliation: Institut Fourier, Laboratoire de Mathématiques, UMR 5582 (UJF-CNRS), BP 74, 38402 St Martin d’Hères Cedex, France
Email: Laurent.Manivel@ujf-grenoble.fr

DOI: https://doi.org/10.1090/S1056-3911-07-00440-7
Received by editor(s): September 26, 2005
Received by editor(s) in revised form: November 9, 2005
Published electronically: February 6, 2007
Additional Notes: Partially supported by grant MI-1503/2005 of the Bulgarian Foundation for Scientific Research

American Mathematical Society