Equivariant $G$-structure on versal deformations
HTML articles powered by AMS MathViewer
- by Dock S. Rim PDF
- Trans. Amer. Math. Soc. 257 (1980), 217-226 Request permission
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
-
A. Grothendieck, Séminaire de géométrie algébrique. II, Exp. 6, Inst. Hautes Etudes Sci., Paris, 1960-1961.
â, Techniques de construction et thĂ©orĂšmes dâexistence en gĂ©omĂ©trie algĂ©brique. IV: les schĂšmes de Hilbert, Seminaire Bourbaki, Exp. 221, SecrĂ©tariat Math., Paris, 1961.
- H. C. Pinkham, Deformations of cones with negative grading, J. Algebra 30 (1974), 92â102. MR 347822, DOI 10.1016/0021-8693(74)90194-X â, Deformations of algebraic varieties with ${G_m}$ action, AstĂ©rique No. 20, Soc. Math. France, Paris, 1974. Dock S. Rim, Formal moduli of deformation, Lecture Notes in Math., vol. 288, Springer-Verlag, Berlin and New York, 1972, pp. 32-132.
- D. S. Rim, Torsion differentials and deformation, Trans. Amer. Math. Soc. 169 (1972), 257â278. MR 342513, DOI 10.1090/S0002-9947-1972-0342513-4
- Dock Sang Rim and Marie A. Vitulli, Weierstrass points and monomial curves, J. Algebra 48 (1977), no. 2, 454â476. MR 457447, DOI 10.1016/0021-8693(77)90322-2
- Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208â222. MR 217093, DOI 10.1090/S0002-9947-1968-0217093-3
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 257 (1980), 217-226
- MSC: Primary 14D15
- DOI: https://doi.org/10.1090/S0002-9947-1980-0549162-8
- MathSciNet review: 549162