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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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Equisingular deformations of plane algebroid curves
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by Jonathan M. Wahl PDF
Trans. Amer. Math. Soc. 193 (1974), 143-170 Request permission

Abstract:

We construct a formal versal equisingular deformation of a plane algebroid curve (in characteristic zero), and show it is smoothly embedded in the whole deformation space of the singularity. Closer analysis relates equisingular deformations of the curve to locally trivial deformations of a certain (nonreduced) projective curve. Finally, we prove that algebraic ${\pi _1}$ of the complement of a plane algebroid curve remains constant during formal equisingular deformation.
References
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Additional Information
  • © Copyright 1974 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 193 (1974), 143-170
  • MSC: Primary 14D15; Secondary 14H20
  • DOI: https://doi.org/10.1090/S0002-9947-1974-0419439-2
  • MathSciNet review: 0419439