Title:
On Q-conic bundles
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.
Jointly with Yuri Prokhorov, we study the structure of
Q-conic bundles near their singular fibers.
We show 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 further the complete classification of Q-conic
bundles under the additional assumption that
the base surface is singular.
Shigefumi Mori