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

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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 2, Pages 3–10
DOI: https://doi.org/10.4213/faa2897 (Mi faa2897)

This article is cited in 17 scientific papers (total in 17 papers)

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

S. M. Gusein-Zade^a, F. Delgado^b, A. Campillo^b

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

Full-text PDF (195 kB) Citations (17)

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

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.

Received: 22.10.2007

English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 2, Pages 83–88
DOI: https://doi.org/10.1007/s10688-008-0013-7

Bibliographic databases:

Document Type: Article

UDC: 512.774.1

Language: Russian

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

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https://doi.org/10.4213/faa2897

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This publication is cited in the following 17 articles:

János Nagy, András Némethi, “The Abel map for surface singularities III: Elliptic germs”, Math. Z., 300:2 (2022), 1753
János Nagy, András Némethi, Contemporary Mathematics, 778, 𝑝-Adic Analysis, Arithmetic and Singularities, 2022, 259
András Némethi, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, 74, Normal Surface Singularities, 2022, 345
José Cogolludo-Agustín, Tamás László, Jorge Martín-Morales, András Némethi, Contemporary Mathematics, 778, 𝑝-Adic Analysis, Arithmetic and Singularities, 2022, 231
Tamás László, János Nagy, András Némethi, “Surgery formulae for the Seiberg–Witten invariant of plumbed 3-manifolds”, Rev Mat Complut, 33:1 (2020), 197
Laszlo T., Szilagyi Z., “On Poincare Series Associated With Links of Normal Surface Singularities”, Trans. Am. Math. Soc., 372:9 (2019), 6403–6436
Tamás László, János Nagy, András Némethi, “Combinatorial duality for Poincaré series, polytopes and invariants of plumbed 3-manifolds”, Sel. Math. New Ser., 25:2 (2019)
János Nagy, András Némethi, “The Abel map for surface singularities I: generalities and examples”, Math. Ann., 375:3-4 (2019), 1427
Francisco Monserrat, Sebastià Xambó-Descamps, Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, 2018, 1
Laszlo T., Szilagyi Z., “Non-Normal Affine Monoids, Modules and Poincaré Series of Plumbed 3-Manifolds”, Acta Math. Hung., 152:2 (2017), 421–452
Laszlo T., Nemethi A., “Reduction Theorem For Lattice Cohomology”, Int. Math. Res. Notices, 2015, no. 11, 2938–2985
Laszlo T., Nemethi A., “Ehrhart Theory of Polytopes and Seiberg-Witten Invariants of Plumbed 3-Manifolds”, Geom. Topol., 18:2 (2014), 717–778
Campillo A., Delgado F., Gusein-Zade S.M., “Equivariant Poincaré, Series of Filtrations”, Rev. Mat. Complut., 26:1 (2013), 241–251
Némethi A., “The cohomology of line bundles of splice-quotient singularities”, Adv. Math., 229:4 (2012), 2503–2524
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
Némethi A., “The Seiberg-Witten invariants of negative definite plumbed 3-manifolds”, J. Eur. Math. Soc. (JEMS), 13:4 (2011), 959–974
S. M. Gusein-Zade, “Integration with respect to the Euler characteristic and its applications”, Russian Math. Surveys, 65:3 (2010), 399–432

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Functional Analysis and Its Applications

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