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TitleInvariant deformation theory of affine schemes with reductive group action
Author(s) Christian Lehn, Ronan Terpereau
TypeArticle in Journal
AbstractAbstract 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 ⊂ 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 we describe their singularities.
URL http://www.sciencedirect.com/science/article/pii/S0022404915000304
JournalJournal of Pure and Applied Algebra
Pages4168 - 4202
Translation No
Refereed No