On -conic Bundles

  • Shigefumi Mori

    Kyoto University, Japan
  • Yuri Prokhorov

    Moscow State University, Russian Federation


A -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 -conic bundles near their singular fibers. One corollary to our main results is that the base surface of every -conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain the complete classification of -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 -conic Bundles. Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, pp. 315–369

DOI 10.2977/PRIMS/1210167329