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Transactions of the American Mathematical Society

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

 

 

Equisingular deformations of plane algebroid curves


Author: Jonathan M. Wahl
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
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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.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0419439-2
Keywords: Plane algebroid curve, equisingularity, deformation space, infinitesimal deformation, algebraic fundamental group
Article copyright: © Copyright 1974 American Mathematical Society