A 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 ℚ-conic bundles near their singular ﬁbers. One corollary to our main results is that the base surface of every 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 ℚ-conic bundles under the additional assumption that the singular ﬁber is irreducible and the base surface is singular.
Cite this article
Shigefumi Mori, Yuri Prokhorov, On ℚ-conic Bundles. Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, pp. 315–369DOI 10.2977/PRIMS/1210167329