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

Author(s): Atanas Iliev; Laurent Manivel
Journal: J. Algebraic Geom. 16 (2007), 499-530.
Posted: February 6, 2007
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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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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

PII: S 1056-3911(07)00440-7
Received by editor(s): September 26, 2005
Received by editor(s) in revised form: November 9, 2005
Posted: February 6, 2007
Additional Notes: Partially supported by grant MI-1503/2005 of the Bulgarian Foundation for Scientific Research

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