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A lower bound for the number of components of the moduli schemes of stable rank 2 vector bundles on projective 3-folds
Author(s):
E.
Ballico;
R.
M.
Miró-Roig
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2557-2560.
MSC (1991):
Primary 14J60, 14F05
Posted:
May 4, 1999
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Abstract:
Fix a smooth projective 3-fold , , with ample, and . Assume the existence of integers with such that is numerically equivalent to . Let be the moduli scheme of -stable rank 2 vector bundles, , on with and . Let be the number ofits irreducible components. Then .
References:
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- V. Ancona and G. Ottaviani, The Horrocks bundles of rank
on , J. Reine Angew. Math. 460 (1995), 69-92. MR 96d:14038 - [E]
- L. Ein, Generalized null correlations bundles, Nagoya Math. J. 111 (1988), 13-24. MR 89k:14024
- [GL]
- D. Gieseker and J. Li, Irreducibility of moduli of rank two vector bundles, J. Diff. Geom. 40 (1994), 23-104. MR 95f:14068
- [Gr]
- A. Grothendieck, Sur quelques points d'algèbre homologique, Tohoku Math. J. 9 (1957), 119-221. MR 21:1328
- [L]
- H. Lange, On stable and ample vector bundles of rank
on curves, Math. Ann. 238 (1978), 193-202. MR 80c:14012 - [O]
- K. O'Grady, Moduli of vector bundles on projective surfaces: some basic results, Invent. Math. 123 (1996), 141-207. MR 96k:14004
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Additional Information:
E.
Ballico
Affiliation:
Department of Mathematics, University of Trento, 38050 Povo, Trento, Italy
Email:
ballico@science.unitn.it
R.
M.
Miró-Roig
Affiliation:
Departamento de Algebra i Geometria, Universitat de Barcelona, Gran Via 585, 008007 Barcelona, Spain
Email:
miro@cerber.ub.es
DOI:
10.1090/S0002-9939-99-05402-7
PII:
S 0002-9939(99)05402-7
Keywords:
Vector bundle,
stable vector bundle,
moduli scheme,
$H$-stable vector bundle,
projective 3-fold,
stability
Received by editor(s):
October 4, 1997
Posted:
May 4, 1999
Communicated by:
Ron Donagi
Copyright of article:
Copyright
1999,
American Mathematical Society
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