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This article is cited in 1 scientific paper (total in 1 paper)
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.
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
Linking options:
https://www.mathnet.ru/eng/faa3043https://doi.org/10.4213/faa3043 https://www.mathnet.ru/eng/faa/v45/i4/p40
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Abstract page: | 456 | Full-text PDF : | 169 | References: | 71 | First page: | 19 |
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