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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Deformations of generalized complete intersections


Authors: R. Mandelbaum and M. Schaps
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
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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 [Enhancements On Off] (What's this?)

  • [D] Laksov, Deformation of determinantal varieties, Univ. of Oslo (to appear).
  • [M] Schaps, Deformations of Cohen-Macaulay schemes of codimension $ 2$ and non-singular deformations of space curves (to appear). MR 0491715 (58:10918)
  • [M] Schlessinger, Functors of Artin rings, Trans. Amer. Math. Soc. 130 (1968), 208-222. MR 36 #184. MR 0217093 (36:184)

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DOI: https://doi.org/10.1090/S0002-9939-1976-0429888-1
Article copyright: © Copyright 1976 American Mathematical Society

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