Deformations of generalized complete intersections
HTML articles powered by AMS MathViewer
- by R. Mandelbaum and M. Schaps PDF
- Proc. Amer. Math. Soc. 61 (1976), 7-10 Request permission
Abstract:
The concept of a generalized complete intersection (GCI) of affine schemes is introduced. The proofs of the following theorems are then sketched. Theorem 1. Suppose $X$ is a $GCI$ of affine Cohen-Macaulay schemes of codimension $\leqslant 2$. Then if the versal deformation space of $X$ exists, it is smooth. Theorem 2. Suppose $X$ is a $GCI$ of determinantal schemes. Then if $\dim X$ is sufficiently low, $X$ is smoothable. In particular, if $X$ is as in Theorem 1 and $\dim X < 4$ then $X$ is smoothable.References
-
Laksov, Deformation of determinantal varieties, Univ. of Oslo (to appear).
- Mary Schaps, Deformations of Cohen-Macaulay schemes of codimension $2$ and non-singular deformations of space curves, Amer. J. Math. 99 (1977), no. 4, 669–685. MR 491715, DOI 10.2307/2373859
- Michael Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208–222. MR 217093, DOI 10.1090/S0002-9947-1968-0217093-3
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 7-10
- MSC: Primary 14D15; Secondary 14B05
- DOI: https://doi.org/10.1090/S0002-9939-1976-0429888-1
- MathSciNet review: 0429888