On Q-conic bundles

Details On Q-conic bundles On Q-conic bundles

2006-03-31

arxiv.org/abs/math/0603736v2

Publ. Res. Inst. Math. Sci., 2008, 44, 315-369

Mathematics

Algebraic Geometry

54 pages, LaTeX

Scientific paper

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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