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Izv. RAN. Ser. Mat., 2013, Volume 77, Issue 3, Pages 163–198 (Mi izv7997)  

This article is cited in 5 scientific papers (total in 5 papers)

Covering semigroups

Vik. S. Kulikova, V. M. Kharlamovb

a Steklov Mathematical Institute of the Russian Academy of Sciences
b Université de Strasbourg

Abstract: We introduce and study a semigroup structure on the set of irreducible components of the Hurwitz space of marked coverings of a complex projective curve with given Galois group of the coverings and fixed ramification type. As an application, we give new conditions on the ramification type that are sufficient for the irreducibility of the Hurwitz spaces, suggest some bounds on the number of irreducible components under certain more general conditions, and show that the number of irreducible components coincides with the number of topological classes of the coverings if the number of branch points is big enough.

Keywords: irreducible components of the Hurwitz space of finite-sheeted coverings of projective curves, semigroups over groups.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00185
Ministry of Education and Science of the Russian Federation НШ-4713.2010.1
11.G34.31.0023
Agence Nationale de la Recherche ANR-09-BLAN-0039-01
National Science Foundation 0854989


DOI: https://doi.org/10.4213/im7997

Full text: PDF file (819 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2013, 77:3, 594–626

Bibliographic databases:

Document Type: Article
UDC: 512.53+512.544+512.772.5
MSC: 14H30, 20M50, 57M05
Received: 10.05.2012

Citation: Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. RAN. Ser. Mat., 77:3 (2013), 163–198; Izv. Math., 77:3 (2013), 594–626

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. Kanev, “Irreducible components of Hurwitz spaces parameterizing Galois coverings of curves of positive genus”, Pure Appl. Math. Q., 10:2 (2014), 193–222  crossref  mathscinet  zmath  isi  scopus
    2. F. A. Bogomolov, Vik. S. Kulikov, “The ambiguity index of an equipped finite group”, Eur. J. Math., 1:2 (2015), 260–278  mathnet  crossref  mathscinet  zmath  scopus
    3. F. Catanese, “Topological methods in moduli theory”, Bull. Math. Sci., 5:3 (2015), 287–449  crossref  mathscinet  zmath  isi  elib  scopus
    4. V. I. Zvonilov, S. Yu. Orevkov, “Compactification of the Space of Branched Coverings of the Two-Dimensional Sphere”, Proc. Steklov Inst. Math., 298 (2017), 118–128  mathnet  crossref  crossref  mathscinet  isi  elib
    5. R. Moschetti, G. P. Pirola, “Hurwitz spaces and liftings to the Valentiner group”, J. Pure Appl. Algebra, 222:1 (2018), 19–38  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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