%0 Journal Article
%T On Q-conic bundles
%A Shigefumi Mori
%A Yuri Prokhorov
%J Mathematics
%D 2006
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0603736v2