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Stability of conic bundles - (With an appendix by Mundet I Riera)

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Sols, Ignacio and Gómez, Tomás L. (2000) Stability of conic bundles - (With an appendix by Mundet I Riera). International journal of mathematics, 11 (8). pp. 1027-1055. ISSN 0129-167X

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Official URL: http://www.worldscientific.com/doi/pdf/10.1142/S0129167X00000507




Abstract

Roughly speaking, a conic bundle is a surface, fibered over a curve, such that the fibers are conics (not necessarily smooth). We define stability for conic bundles and construct a moduli space. We prove that (after fixing some invariants) these moduli spaces are irreducible (under some conditions). Conic bundles can be thought of as generalizations of orthogonal bundles on curves. We show that in this particular case our definition of stability agrees with the definition of stability for orthogonal bundles. Finally, in an appendix by I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic bundles.


Item Type:Article
Uncontrolled Keywords:Principal bundles; Algebraic-curves; Moduli
Subjects:Sciences > Mathematics > Algebra
ID Code:20448
Deposited On:15 Mar 2013 18:17
Last Modified:25 Sep 2018 17:19

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