Search results for "13A50"

showing 4 items of 4 documents

Locally nilpotent derivations of rings with roots adjoined

2013

Algebra14L30General MathematicsLocally nilpotent13A5014R2013N15Mathematics
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Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras

2012

The research of the first named author was partially supported by INdAM. The research of the second, third, and fourth named authors was partially supported by Grant for Bilateral Scientific Cooperation between Bulgaria and Ukraine. The research of the fifth named author was partially supported by NSF Grant DMS-1016086.

Classical Invariant Theory05A15 05E05 05E10 13A50 15A72 16R10 16R30 20G05MacMahon Partition AnalysisHilbert SeriesRational symmetric functions classical invariant theory algebras with polynomial identity cocharacter sequenceMathematics - Rings and AlgebrasCommutative Algebra (math.AC)Mathematics - Commutative AlgebraRational Symmetric FunctionsAlgebras with Polynomial IdentitySettore MAT/02 - AlgebraRings and Algebras (math.RA)Noncommutative Invariant TheoryFOS: MathematicsCocharacter SequenceMathematics - CombinatoricsCombinatorics (math.CO)
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Invariant deformation theory of affine schemes with reductive group action

2015

We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.

Classical groupPure mathematicsInvariant Hilbert schemeDeformation theory01 natural sciencesMathematics - Algebraic Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsInvariant (mathematics)Representation Theory (math.RT)Algebraic Geometry (math.AG)MathematicsAlgebra and Number Theory[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010102 general mathematicsReductive group16. Peace & justiceObstruction theoryDeformation theoryHilbert schemeAlgebraic groupMSC: 13A50; 20G05; 14K10; 14L30; 14Q99; 14B12Gravitational singularity010307 mathematical physicsAffine transformation[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]SingularitiesMathematics - Representation Theory
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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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