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

Abstract

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 . To cite this article: P. Popescu-Pampu, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 1101–1106.