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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 266, Pages 218–233 (Mi znsl1254)  
This article is cited in 6 scientific papers (total in 6 papers)

The growth rate of the number of classes of real plane algebraic curves with the growth of the degree

S. Yu. Orevkovab, V. M. Kharlamovc

a Steklov Mathematical Institute, Russian Academy of Sciences
b Université Paul Sabatier
c University Louis Pasteur
Full-text PDF (249 kB) Citations (6)
Abstract: The work presents some results on the asymptotics of the number of real plane algebraic curves as the degree grows. In particular, we obtain the asymptotics of the number of curves considered up to the isotopy and rigid isotopy, as well as the number of isotopic classes of maximal curves realizable by $T$-curves. Some results are generalized onto hypersurfaces in non-singular algebraic varieties of arbitrary dimension.
Received: 10.10.1999
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 113, Issue 5, Pages 666–674
DOI: https://doi.org/10.1023/A:1021158529011
Bibliographic databases:
Document Type: Article
UDC: 512.77
Language: Russian
Citation: S. Yu. Orevkov, V. M. Kharlamov, “The growth rate of the number of classes of real plane algebraic curves with the growth of the degree”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part V, Zap. Nauchn. Sem. POMI, 266, POMI, St. Petersburg, 2000, 218–233; J. Math. Sci. (N. Y.), 113:5 (2003), 666–674
Citation in format AMSBIB
\Bibitem{OreKha00}
\by S.~Yu.~Orevkov, V.~M.~Kharlamov
\paper The growth rate of the number of classes of real plane algebraic curves with the growth of the degree
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~V
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 266
\pages 218--233
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1254}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1774655}
\zmath{https://zbmath.org/?q=an:1067.14518|1026.14017}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 113
\issue 5
\pages 666--674
\crossref{https://doi.org/10.1023/A:1021158529011}
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  • https://www.mathnet.ru/eng/znsl/v266/p218
    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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