Stability of conic bundles (with an appendix by Mundet i Riera)

Details Stability of conic bundles (with an appendix by Mundet i Riera) Stability of conic bundles (with an appendix by Mundet i Riera)

1999-11-25

arxiv.org/abs/math/9911198v1

Mathematics

Algebraic Geometry

24 pages, LaTeX2e

Scientific paper

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.

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