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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Deformations of formal embeddings of schemes
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by Miriam P. Halperin PDF
Trans. Amer. Math. Soc. 221 (1976), 303-321 Request permission

Abstract:

A family of isolated singularities of k-varieties will be here called equisingular if it can be simultaneously resolved to a family of hypersurfaces embedded in nonsingular spaces which induce only locally trivial deformations of pairs of schemes over local artin k-algebras. The functor of locally trivial deformations of the formal embedding of an exceptional set has a versal object in the sense of Schlessinger. When the exceptional set ${X_0}$ is a collection of nonsingular curves meeting normally in a nonsingular surface X, the moduli correspond to Laufer’s moduli of thick curves. When X is a nonsingular scheme of finite type over an algebraically closed field k and ${X_0}$ is a reduced closed subscheme of X, every deformation of $(X,{X_0})$ to $k[\varepsilon ]$ such that the deformation of ${X_0}$ is locally trivial, is in fact a locally trivial deformation of pairs.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 221 (1976), 303-321
  • MSC: Primary 14D15; Secondary 14E15
  • DOI: https://doi.org/10.1090/S0002-9947-1976-0407016-0
  • MathSciNet review: 0407016