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

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

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Document Type: Article
MSC: 14H30

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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Citing articles on Google Scholar: Russian citations, English citations
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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
2. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275
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
4. Degtyarev A., “Topology of plane algebraic curves: the algebraic approach”, Topology of Algebraic Varieties and Singularities, Contemporary Mathematics, 538, 2011, 137–161
5. Duc Tai Pho, “Alexander Polynomials of Certain Dual of Smooth Quartics”, Proc. Jpn. Acad. Ser. A-Math. Sci., 89:9 (2013), 119–122
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
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
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