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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 143–162 (Mi izv16)  

This article is cited in 3 scientific papers (total in 3 papers)

On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve

Vik. S. Kulikova, V. S. Kulikovb

a Moscow State Academy of Printing Arts
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The semisimplicity is proved of the Alexander automorphism (the monodromy operator) on the cohomology $H^1(X_\infty)_{\ne 1}$ of the infinite cyclic covering of the complement to a plane non-reduced algebraic curve, and, in particular, the semisimplicity of $H^1(X_\infty)$ in the case of an irreducible curve. A natural mixed Hodge structure on $H^1(X_\infty)$ is introduced and the irregularity of cyclic coverings of $P^2$ is calculated in terms of the number of roots of the Alexander polynomial of the branch curve.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 367–386

Bibliographic databases:

MSC: 14H30
Received: 11.10.1994

Citation: Vik. S. Kulikov, V. S. Kulikov, “On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a plane algebraic curve”, Izv. RAN. Ser. Mat., 59:2 (1995), 143–162; Izv. Math., 59:2 (1995), 367–386

Citation in format AMSBIB
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\by Vik.~S.~Kulikov, V.~S.~Kulikov
\paper On the monodromy and mixed Hodge structure on cohomology of the infinite cyclic covering of the complement to a~plane algebraic curve
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 143--162
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1337163}
\zmath{https://zbmath.org/?q=an:0909.14004}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 367--386
\crossref{https://doi.org/10.1070/IM1995v059n02ABEH000016}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800007}


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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. Vik. S. Kulikov, “On plane algebraic curves of positive Albanese dimension”, Izv. Math., 59:6 (1995), 1173–1192  mathnet  crossref  mathscinet  zmath  isi
    2. G.-M. Greuel, Vik. S. Kulikov, “On symplectic coverings of the projective plane”, Izv. Math., 69:4 (2005), 667–701  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Dimca A., Libgober A., “Regular Functions Transversal at Infinity”, Tohoku Math. J., 58:4 (2006), 549–564  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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