Poincare series of filtrations corresponding to ideals on surfaces

A. Campillo; F. Delgado; S. M. Gusein-Zade

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arXiv · 0803.1743

Poincare series of filtrations corresponding to ideals on surfaces

A. Campillo·F. Delgado·S. M. Gusein-Zade

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Abstract

Earlier the authors considered and, in some cases, computed Poincare series of 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 from the first class was defined by a curve (with several branches) on the surface singularity. The other one (so called divisorial filtration) was defined by a set of components of the exceptional divisor of a modification of the surface singularity. Here we define a filtration corresponding to an ideal or to a set of ideals in the ring of germs of functions on a surface singularity and compute the corresponding Poincare series in some cases. For the complex plane this notion unites the two classes of filtrations described above.

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BibTeX RIS

A. Campillo, F. Delgado, S. M. Gusein-Zade. 2008-09-12. Poincare series of filtrations corresponding to ideals on surfaces. https://arxiv.org/abs/0803.1743

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