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
Full-text PDF
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
.
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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