Pfaffian lines and vector bundles on Fano threefolds of genus 8

Iliev, Atanas; Manivel, Laurent

doi:10.1090/S1056-3911-07-00440-7

Pfaffian lines and vector bundles on Fano threefolds of genus

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 | References | Additional Information

Abstract: Let be a general complex Fano threefold of genus . We prove that the moduli space of rank two semistable sheaves on with Chern numbers , and is isomorphic to the Fano surface of conics on . This surface is smooth and isomorphic to the Fano surface of lines in the orthogonal to cubic threefold. Inside , the nonlocally free sheaves are parameterized by a smooth curve of genus isomorphic to the base of the family of lines on $\textrm{X}$ .

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Additional Information

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