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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 2, Pages 3–10 (Mi faa2897)  

This article is cited in 8 scientific papers (total in 8 papers)

Universal Abelian Covers of Rational Surface Singularities and Multi-Index Filtrations

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

a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b University of Valladolid

Abstract: In previous papers, the authors computed the Poincaré series of some (multi-index) filtrations on the ring of germs of functions on a rational surface singularity. These Poincaré series were expressed as the integer parts of certain fractional power series, whose interpretation was not given. In this paper, we show that, up to a simple change of variables, these fractional power series are reductions of the equivariant Poincaré series for filtrations on the ring of germs of functions on the universal Abelian cover of the surface. We compute these equivariant Poincaré series.

Keywords: universal Abelian cover, rational surface singularity, Poincaré series

DOI: https://doi.org/10.4213/faa2897

Full text: PDF file (195 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:2, 83–88

Bibliographic databases:

UDC: 512.774.1
Received: 22.10.2007

Citation: S. M. Gusein-Zade, F. Delgado, A. Campillo, “Universal Abelian Covers of Rational Surface Singularities and Multi-Index Filtrations”, Funktsional. Anal. i Prilozhen., 42:2 (2008), 3–10; Funct. Anal. Appl., 42:2 (2008), 83–88

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. M. Gusein-Zade, “Integration with respect to the Euler characteristic and its applications”, Russian Math. Surveys, 65:3 (2010), 399–432  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. S. M. Gusein-Zade, F. Delgado, A. Campillo, “Alexander polynomials and Poincaré series of sets of ideals”, Funct. Anal. Appl., 45:4 (2011), 271–277  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Némethi A., “The Seiberg-Witten invariants of negative definite plumbed 3-manifolds”, J. Eur. Math. Soc. (JEMS), 13:4 (2011), 959–974  crossref  mathscinet  zmath  isi
    4. Némethi A., “The cohomology of line bundles of splice-quotient singularities”, Adv. Math., 229:4 (2012), 2503–2524  crossref  mathscinet  zmath  isi  elib
    5. Campillo A., Delgado F., Gusein-Zade S.M., “Equivariant Poincaré, Series of Filtrations”, Rev. Mat. Complut., 26:1 (2013), 241–251  crossref  mathscinet  zmath  isi
    6. Laszlo T., Nemethi A., “Ehrhart Theory of Polytopes and Seiberg-Witten Invariants of Plumbed 3-Manifolds”, Geom. Topol., 18:2 (2014), 717–778  crossref  mathscinet  zmath  isi  elib
    7. Laszlo T., Nemethi A., “Reduction Theorem For Lattice Cohomology”, Int. Math. Res. Notices, 2015, no. 11, 2938–2985  crossref  mathscinet  zmath  isi  elib
    8. Laszlo T., Szilagyi Z., “Non-Normal Affine Monoids, Modules and Poincaré Series of Plumbed 3-Manifolds”, Acta Math. Hung., 152:2 (2017), 421–452  crossref  mathscinet  zmath  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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