Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

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
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: Fix a smooth projective 3-fold $X$, $c_1$, $H\in\mathrm{Pic}(X)$ with $H$ ample, and $d\in\mathbf{Z}$. Assume the existence of integers $a,b$ with $a\not=0$ such that $ac_1$ is numerically equivalent to $bH$. Let $M(X,2,c_1,d,H)$ be the moduli scheme of $H$-stable rank 2 vector bundles, $E$, on $X$ with $c_1(E)=c_1$ and $c_2(E)\cdot H=d$. Let $m(X,2,c_1,d,H)$ be the number ofits irreducible components. Then $\limsup _{d\rightarrow\infty}m(X,2,c_1,d,H)= +\infty$.


References:

[AO]
V. Ancona and G. Ottaviani, The Horrocks bundles of rank $3$ on $\mathbf{P}^5$, 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 $2$ 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


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 14J60, 14F05

Retrieve articles in all Journals with MSC (1991): 14J60, 14F05


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


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google