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Статья

Quotients of conic bundles

Transformation Groups. 2016. Vol. 21. No. 1. P. 275-295.

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over P 1 k by finite groups of automorphisms. We construct smooth minimal models for such quotients. We show that any quotient is birationally equivalent to a quotient of other k-rational conic bundle cyclic group C2 k of order 2k , dihedral group D2 k of order 2k , alternating group A4 of degree 4, symmetric group S4 of degree 4 or alternating group A5 of degree 5 effectively acting on the base of the conic bundle. Also we construct infinitely many examples of such quotients which are not k-birationally equivalent to each other.