Search results for "14B12"

showing 2 items of 2 documents

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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Algebraic singularities have maximal reductive automorphism groups

1989

LetX = On/ibe an analytic singularity where ṫ is an ideal of theC-algebraOnof germs of analytic functions on (Cn, 0). Letdenote the maximal ideal ofXandA= AutXits group of automorphisms. An abstract subgroupequipped with the structure of an algebraic group is calledalgebraic subgroupofAif the natural representations ofGon all “higher cotangent spaces”are rational. Letπbe the representation ofAon the first cotangent spaceandA1=π(A).

p-groupPure mathematics32B30010308 nuclear & particles physicsGeneral Mathematics010102 general mathematicsOuter automorphism groupCotangent spaceReductive groupAutomorphism01 natural sciences14B12Inner automorphismAlgebraic group0103 physical sciencesComputingMethodologies_DOCUMENTANDTEXTPROCESSINGMaximal ideal13J1520G200101 mathematics32M05MathematicsNagoya Mathematical Journal
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