On the analytical invariance of the semigroups of a quasi-ordinary hypersurface singularity

Patrick Popescu-Pampu (1)

1 IMJ - Institut de Mathématiques de Jussieu

We associate to any irreducible germ S of complex quasi-ordinary hypersurface an analytically invariant semigroup. We deduce a direct proof (without passing through their embedded topological invariance) of the analytical invariance of the normalized characteristic exponents. These exponents generalize the generic Newton-Puiseux exponents of plane curves. Incidentally, we give a toric description of the normalization morphism of the germ S.

Domains: Complex Variables [math.CV]; Algebraic Geometry [math.AG]

Patrick Popescu-Pampu. On the analytical invariance of the semigroups of a quasi-ordinary hypersurface singularity. Duke Mathematical Journal, 2004, 124, pp.67-104. ⟨hal-00133227⟩