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 Relative Articles On Q-conic bundles, II On Q-conic bundles, III Stable rationality and conic bundles Conic bundles and Clifford algebras Topology of Conic Bundles - II Quotients of conic bundles Rationality problem of conic bundles Counting Multisections in Conic Bundles over a Curve defined over F_q Stability of conic bundles (with an appendix by Mundet i Riera) Minimal sections of conic bundles More...
Mathematics  2006

# On Q-conic bundles

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Abstract:

A \$\mathbb Q\$-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of \$\mathbb Q\$-conic bundles near their singular fibers. One corollary to our main results is that the base surface of every \$\mathbb Q\$-conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain the complete classification of \$\mathbb Q\$-conic bundles under the additional assumption that the singular fiber is irreducible and the base surface is singular.

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