Quotients of conic bundles

Andrey Trepalin

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arXiv · 1312.6867

Quotients of conic bundles

Andrey Trepalin

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Abstract

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over projective line 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 of order $2^k$, dihedral group of order $2^k$, alternating group of degree $4$, symmetric group of degree $4$ or alternating group of degree $5$ effectively acting on the base of conic bundle. Also we construct infinitely many examples of such quotients which are not k-birationally equivalent to each other.

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Andrey Trepalin. 2013-12-24. Quotients of conic bundles. https://arxiv.org/abs/1312.6867

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