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Transactions of the American Mathematical Society

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



Equisingular deformations of Puiseux expansions

Author: Augusto Nobile
Journal: Trans. Amer. Math. Soc. 214 (1975), 113-135
MSC: Primary 14H20; Secondary 14D15
MathSciNet review: 0414560
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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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Keywords: Branch, Puiseux expansion, deformation parametrization, characteristic of a parametrization, equisingular deformation, versal deformation, formal family of branches, <IMG WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$\nu$">-truncation of a family
Article copyright: © Copyright 1975 American Mathematical Society