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. Building upon our previous paper [MP08a], we prove the existence of a Du Val anti-canonical member under the assumption that the central fiber is irreducible.
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Shigefumi Mori, Yuri Prokhorov, On ℚ-Conic Bundles, III. Publ. Res. Inst. Math. Sci. 45 (2009), no. 3, pp. 787–810DOI 10.2977/PRIMS/1249478965