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Funktsional. Anal. i Prilozhen., 2011, Volume 45, Issue 4, Pages 40–48 (Mi faa3043)  

Alexander polynomials and Poincaré series of sets of ideals

S. M. Gusein-Zadea, F. Delgadob, A. Campillob

a Faculty of Mathematics and Mechanics, Moscow State University, Moscow, Russia
b Department of Algebra, Geometry and Topology, University of Valladolid, Valladolid, Spain

Abstract: Earlier the authors considered and, in some cases, computed Poincaré series for two sorts of multi-index filtrations on the ring of germs of functions on a complex (normal) surface singularity (in particular, on the complex plane). A filtration of the first class was defined by a curve (with several branches) on the surface singularity. A filtration of the second class (called divisorial) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define and compute in some cases the Poincaré series corresponding to a set of ideals in the ring of germs of functions on a surface singularity. For the complex plane, this notion unites the two classes of filtrations described above.

Keywords: ideal, surface, Poincaré series, zeta function.

DOI: https://doi.org/10.4213/faa3043

Full text: PDF file (202 kB)
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English version:
Functional Analysis and Its Applications, 2011, 45:4, 271–277

Bibliographic databases:

UDC: 512.717
Received: 23.01.2011

Citation: S. M. Gusein-Zade, F. Delgado, A. Campillo, “Alexander polynomials and Poincaré series of sets of ideals”, Funktsional. Anal. i Prilozhen., 45:4 (2011), 40–48; Funct. Anal. Appl., 45:4 (2011), 271–277

Citation in format AMSBIB
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