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Izvestiya: Mathematics, 2013, Volume 77, Issue 3, Pages 594–626
DOI: https://doi.org/10.1070/IM2013v077n03ABEH002651 (Mi im7997) 		 
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
English version PDF (521 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/IM2013v077n03ABEH002651
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
Received: 10.05.2012
Bibliographic databases:
Document Type: Article
UDC: 512.53+512.544+512.772.5
MSC: 14H30, 20M50, 57M05
Language: English
Original paper language: Russian
Citation: Vik. S. Kulikov, V. M. Kharlamov, “Covering semigroups”, Izv. Math., 77:3 (2013), 594–626
Citation in format AMSBIB
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\by Vik.~S.~Kulikov, V.~M.~Kharlamov
\paper Covering semigroups
\jour Izv. Math.
\yr 2013
\vol 77
\issue 3
\pages 594--626
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\crossref{https://doi.org/10.1070/IM2013v077n03ABEH002651}
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Linking options:
  • https://www.mathnet.ru/eng/im7997
  • https://doi.org/10.1070/IM2013v077n03ABEH002651
  • https://www.mathnet.ru/eng/im/v77/i3/p163
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:661
    Russian version PDF:164
    English version PDF:10
    References:79
    First page:41
     
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