JournalsprimsVol. 44, No. 2pp. 315–369

On ℚ-conic Bundles

  • Shigefumi Mori

    Kyoto University, Japan
  • Yuri Prokhorov

    Moscow State University, Russian Federation
On ℚ-conic Bundles cover
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Abstract

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. 315–369

DOI 10.2977/PRIMS/1210167329