Universidad Complutense de Madrid
E-Prints Complutense

Quasi-ordinary singularities, essential divisors and Poincaré series



Último año

González Pérez, Pedro Daniel y Hernando, F. (2009) Quasi-ordinary singularities, essential divisors and Poincaré series. Journal of the London Mathematical Society. Second Series, 79 (3). pp. 780-802. ISSN 0024-6107

Vista previa

URL Oficial: http://jlms.oxfordjournals.org/


We define Poincaré series associated to a germ (S, 0) of toric or analytically irreducible quasiordinary hypersurface singularity, by a finite sequence of monomial valuations such that at least one of them is centered at the point 0. This involves the definition of a multi-graded ring associated to the analytic algebra of the singularity by the sequence of valuations. We prove that the Poincar´e series is a rational function with integer coefficients, which can also be defined as an integral with respect to the Euler characteristic of a function defined by the valuations, over the projectivization of the analytic algebra of the singularity. In particular, the Poincaré series associated to the set of divisorial valuations of the essential divisors, considered both over the singular locus and over the point 0, is an analytic invariant of the singularity. In the quasi-ordinary hypersurface case we prove that this Poincar´e series determines and is determined by the normalized sequence of characteristic monomials. These monomials in the analytic case define a complete invariant of the embedded topological type of the hypersurface singularity.

Tipo de documento:Artículo
Palabras clave:Quasi-ordinary singularities; Poincaré series; Multi-graded rings; Valuations; Divisorial valuations; Characteristic monomials; Hypersurface singularities; Nash map; Toric singularities
Materias:Ciencias > Matemáticas > Geometria algebraica
Código ID:12580
Depositado:13 Abr 2011 08:45
Última Modificación:06 Feb 2014 09:27

Descargas en el último año

Sólo personal del repositorio: página de control del artículo