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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 6, Pages 75–94 (Mi izv53)  

This article is cited in 7 scientific papers (total in 7 papers)

On plane algebraic curves of positive Albanese dimension

Vik. S. Kulikov

Moscow State University of Railway Communications

Abstract: A notion of Albanese dimension of a plane algebraic curve is introduced as the maximum of the dimensions of the images of Albanese mapping of cyclic coverings of the plane ramified along this curve. A necessary condition for a curve to have Albanese dimension equal to one is given in terms of its equation. This condition is sufficient for a generic curve. A complete description of the Alexander polynomials of plane curves of Albanese dimension one is given. Also the images of the Albanese mappings of cyclic coverings ramified along such curves are described completely.

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English version:
Izvestiya: Mathematics, 1995, 59:6, 1173–1192

Bibliographic databases:

Document Type: Article
MSC: 14H30
Received: 04.04.1995

Citation: Vik. S. Kulikov, “On plane algebraic curves of positive Albanese dimension”, Izv. RAN. Ser. Mat., 59:6 (1995), 75–94; Izv. Math., 59:6 (1995), 1173–1192

Citation in format AMSBIB
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\by Vik.~S.~Kulikov
\paper On plane algebraic curves of positive Albanese dimension
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 6
\pages 75--94
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\zmath{https://zbmath.org/?q=an:0939.14013}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 6
\pages 1173--1192
\crossref{https://doi.org/10.1070/IM1995v059n06ABEH000053}
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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. Tokunaga H., “Irreducible Plane Curves with the Albanese Dimension 2”, Proc. Amer. Math. Soc., 127:7 (1999), 1935–1940  crossref  mathscinet  zmath  isi
    2. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Ishida H. Tokunaga H.-o., “Triple Covers of Algebraic Surfaces and a Generalization of Zariski's Example”, Singularities - Niigata - Toyama 2007, Advanced Studies in Pure Mathematics, 56, ed. Brasselet J. Ishi S. Suwa T. Vaquie M., Math Soc Japan, 2009, 169–185  mathscinet  zmath  isi
    4. Degtyarev A., “Topology of plane algebraic curves: the algebraic approach”, Topology of Algebraic Varieties and Singularities, Contemporary Mathematics, 538, 2011, 137–161  crossref  isi
    5. Duc Tai Pho, “Alexander Polynomials of Certain Dual of Smooth Quartics”, Proc. Jpn. Acad. Ser. A-Math. Sci., 89:9 (2013), 119–122  crossref  isi
    6. Cogolludo-Agustin J.-I., Libgober A., “Mordell–Weil groups of elliptic threefolds and the Alexander module of plane curves”, J. Reine Angew. Math., 697 (2014), 15–55  crossref  mathscinet  zmath  isi  scopus
    7. Shirane T., “A note on normal triple covers over P2 with branch divisors of degree 6”, Kodai. Math. J., 37:2 (2014), 330–340  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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