On the invariance of the semigroup of a quasi-ordinary surface singularity

Patrick Popescu-Pampu

doi:10.1016/S1631-073X(02)02404-4

On the invariance of the semigroup of a quasi-ordinary surface singularity
[Sur l'invariance du semi-groupe d'une singularité quasi-ordinaire de surface]

Patrick Popescu-Pampu ¹

¹ ENS Lyon (UMPA), 46, allée d'Italie, 69364 Lyon cedex, France

Comptes Rendus. Mathématique, Volume 334 (2002) no. 12, pp. 1101-1106.

Résumé
Abstract

Nous donnons une preuve algébrique dans le cas des germes bidimensionnels de l'invariance analytique d'un semi-groupe associé par González Pérez à tout germe quasi-ordinaire irréductible $𝒮$ d'hypersurface complexe. Nous en déduisons une nouvelle preuve de l'invariance analytique des exposants caractéristiques normalisés. De plus, nous associons des valeurs dans le semi-groupe aux éléments d'un sous-ensemble de l'algèbre locale de $𝒮$ .

We give an algebraic proof for 2-dimensional germs of the analytic invariance of a semigroup associated by González Pérez to any irreducible germ $𝒮$ of complex quasi-ordinary hypersurface. We deduce from it a new proof of the analytic invariance of the normalized characteristic exponents. Moreover, we associate values in the semigroup to the elements of a subset of the local algebra of $𝒮$ .

Reçu le : 2002-04-09
Accepté le : 2002-04-15
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02404-4

Affiliations des auteurs :

Patrick Popescu-Pampu ¹

¹ ENS Lyon (UMPA), 46, allée d'Italie, 69364 Lyon cedex, France

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Patrick Popescu-Pampu. On the invariance of the semigroup of a quasi-ordinary surface singularity. Comptes Rendus. Mathématique, Volume 334 (2002) no. 12, pp. 1101-1106. doi : 10.1016/S1631-073X(02)02404-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02404-4/

Bibliographie
Cité par

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André Belotto da Silva; Lorenzo Fantini; Anne Pichon On Lipschitz normally embedded complex surface germs, Compositio Mathematica, Volume 158 (2022) no. 3, p. 623 | DOI:10.1112/s0010437x22007357
Patrick Popescu-Pampu On the analytical invariance of the semigroups of a quasi-ordinary hypersurface singularity, Duke Mathematical Journal, Volume 124 (2004) no. 1 | DOI:10.1215/s0012-7094-04-12413-3

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