On Q-conic bundles

Shigefumi Mori; Yuri Prokhorov

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On Q-conic bundles

Shigefumi Mori·Yuri Prokhorov

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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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BibTeX RIS

Shigefumi Mori, Yuri Prokhorov. 2007-08-06. On Q-conic bundles. https://arxiv.org/abs/math/0603736

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