On Q-conic Bundles

By S. Mori, Yuri Prokhorov. 2006

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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 Qconic 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/47ba938550a6691e8e7ecdb480570c3b42e0087a