Search results for " 14R20"

showing 4 items of 4 documents

Locally nilpotent derivations of rings graded by an abelian group

2019

International audience

Russel cubic threefoldPure mathematicsAffine algebraic geometryPham-Brieskorn variety010102 general mathematics[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Locally nilpotent13A50Locally nilpotent derivation01 natural sciences[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]Russell cubic threefold0103 physical sciences010307 mathematical physics[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]0101 mathematicsAbelian group14R20MSC: Primary 14R20 ; Secondary 13A50ComputingMilieux_MISCELLANEOUSMathematics
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Proper triangular Ga-actions on A^4 are translations

2013

We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3.

Algebraaffine spacesMathematics - Algebraic GeometryAlgebra and Number Theorygeometric quotientFOS: Mathematics14L30; 14R20; 14R25[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]Algebraic Geometry (math.AG)proper additive group actionsMathematics[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
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Rationally integrable vector fields and rational additive group actions

2016

International audience; We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar-Limanov invariant…

Integrable systemRationally integrable derivationsGeneral Mathematics010102 general mathematics05 social sciencesLocally nilpotentAlgebraic variety01 natural sciencesLocally nilpotent derivations[ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]AlgebraHomogeneousRational additive group actions0502 economics and businessVector fieldAffine transformation[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]050207 economics0101 mathematicsInvariant (mathematics)MSC: 14E07 14L30 14M25 14R20Additive groupMathematics
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Affine Surfaces With a Huge Group of Automorphisms

2013

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.

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 surfacesQuotientMathematicsInternational Mathematics Research Notices
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