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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A lower bound for the number of components
of the moduli schemes
of stable rank 2 vector bundles
on projective 3-folds


Authors: E. Ballico and R. M. Miró-Roig
Journal: Proc. Amer. Math. Soc. 127 (1999), 2557-2560
MSC (1991): Primary 14J60, 14F05
Published electronically: May 4, 1999
MathSciNet review: 1676315
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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 $\limsup _{d\rightarrow\infty}m(X,2,c_1,d,H)= +\infty$.


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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: http://dx.doi.org/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
Published electronically: May 4, 1999
Communicated by: Ron Donagi
Article copyright: © Copyright 1999 American Mathematical Society