Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 14D15

Retrieve articles in all journals with MSC: 14D15

Additional Information

PII: S 0002-9947(1980)0549162-8
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

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia