Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Equivariant $ G$-structure on versal deformations

Author: Dock S. Rim
Journal: Trans. Amer. Math. Soc. 257 (1980), 217-226
MSC: Primary 14D15
MathSciNet review: 549162
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Abstract: Let $ {X_0}$ be an algebraic variety, and $ (\chi ,\,\Sigma )$ its versal deformation. Now let G be an affine algebraic group acting algebraically on $ {X_0}$. It gives rise to a definite linear G-action on the tangent space of $ \Sigma $. In this paper we establish that if G is linearly reductive then there is an equivariant G-action on $ (\chi ,\Sigma )$ which induces given G-action on the special fibre $ {X_0}$ and its linear G-action on the tangent space of the formal moduli $ \Sigma $. Furthermore, such equivariant G-structure is shown to be unique up to noncanonical isomorphism.

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Keywords: Infinitesimal deformation, formal moduli, versal deformation, linearly reductive group, fibred category in groupoid, cohomology of linearly reductive group
Article copyright: © Copyright 1980 American Mathematical Society