On -conic Bundles
Shigefumi Mori
Kyoto University, JapanYuri Prokhorov
Moscow State University, Russian Federation
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Abstract
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