6533b86ffe1ef96bd12cd255

RESEARCH PRODUCT

Affine Surfaces With a Huge Group of Automorphisms

Jérémy BlancAdrien Dubouloz

subject

Normal subgrouprational fibrationsautomorphismsGroup (mathematics)General Mathematics010102 general mathematicsAutomorphism01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]CombinatoricsMathematics::LogicMathematics - Algebraic GeometryMathematics::Group Theory0103 physical sciencesFree groupCountable setUncountable set[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]010307 mathematical physics0101 mathematicsAlgebraic number14R25 14R20 14R05 14E05affine surfacesQuotientMathematics

description

We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.

yearjournalcountryeditionlanguage
2013-02-15International Mathematics Research Notices
https://doi.org/10.1093/imrn/rnt202