Equisingular deformations of Puiseux expansions

Nobile, Augusto

doi:10.1090/S0002-9947-1975-0414560-8

Equisingular deformations of Puiseux expansions
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by Augusto Nobile

Trans. Amer. Math. Soc. 214 (1975), 113-135

DOI: https://doi.org/10.1090/S0002-9947-1975-0414560-8

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Abstract:

Parametrizations of a deformation (over a complete local ring) of an irreducible algebroid curve are studied. With these parametrizations another definition of equisingularity (equivalent to the known ones) is given, by using their characteristic numbers. These methods are also used in the complex analytic case. The following applications of these techniques are given: a proof of the existence of a versal equisingular deformation in the complex analytic case; a proof that an equisingular formal family of branches is determined by its $\nu$-truncation ($\nu$ large enough, depending only on the characteristic of the special fiber).

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