6533b7dcfe1ef96bd12716d6
RESEARCH PRODUCT
Invariant deformation theory of affine schemes with reductive group action
Christian LehnRonan Terpereausubject
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 Theorydescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-09-01 |