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Transformation Groups

, Volume 21, Issue 1, pp 275–295 | Cite as

QUOTIENTS OF CONIC BUNDLES

  • ANDREY TREPALIN
Article

Abstract

Let k be an arbitrary field of characteristic zero. In this paper we study quotients of k-rational conic bundles over Open image in new window 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 \( {\mathrm{\mathfrak{C}}}_{2^k} \) of order 2 k , dihedral group \( {\mathfrak{D}}_{2^k} \) of order 2 k , alternating group \( {\mathfrak{A}}_4 \) of degree 4, symmetric group \( {\mathfrak{S}}_4 \) of degree 4 or alternating group \( {\mathfrak{A}}_5 \) 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.

Keywords

Galois Group Characteristic Zero Rational Curf Pezzo Surface Rational Surface 
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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsMoscowRussia
  2. 2.Laboratory of Algebraic GeometryNRU-HSEMoscowRussia

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