A ℚ-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ (Z_∌_o) of a normal surface such that ﬁbers are connected and the anti-canonical divisor is relatively ample. We obtain the complete classiﬁcation of ℚ-conic bundle germs when the base surface germ is singular. This is a generalization of [MP08], which further assumed that the ﬁber over o is irreducible.
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Shigefumi Mori, Yuri Prokhorov, On ℚ-conic Bundles, II. Publ. Res. Inst. Math. Sci. 44 (2008), no. 3, pp. 955–971DOI 10.2977/PRIMS/1216238307