Quotients of conic bundles

2013/12/24 by Andrey Trepalin, Trepalin, Andrey · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1312.6867

openalex publication_date 2013/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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