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Zapiski Nauchnykh Seminarov POMI, 2000, Volume 267, Pages 88–118 (Mi znsl1267)  
This article is cited in 1 scientific paper (total in 1 paper)

Real $J$-curves with deep nests on ruled surfaces

J.-Y. Welschinger

Institut de Recherche Mathématique Avancée, Université de Strasbourg
Full-text PDF (353 kB) Citations (1)
Abstract: The paper is divided in two independent parts. The goal of the first part (§ 2) is to present a new proof of the complex orientation formula obtained by S. Yu. Orevkov's [9], which allows one to generalize this formula to $J$-curves with deep nests on ruled surfaces. In particular, this yields an analog of this formula for separating real algebraic curves in $\mathbb C P^2$ with two nests.
In the second part (§ 3), analogs of the inequalities of Arnol'd [1] and Rokhlin [11] are obtained for separating real $J$-curves with deep nests on ruled surfaces.
Received: 06.12.1999
English version:
Journal of Mathematical Sciences (New York), 2003, Volume 113, Issue 6, Pages 777–794
DOI: https://doi.org/10.1023/A:1021227116716
Bibliographic databases:
UDC: 512.77
Language: English
Citation: J.-Y. Welschinger, “Real $J$-curves with deep nests on ruled surfaces”, Geometry and topology. Part 5, Zap. Nauchn. Sem. POMI, 267, POMI, St. Petersburg, 2000, 88–118; J. Math. Sci. (N. Y.), 113:6 (2003), 777–794
Citation in format AMSBIB
\Bibitem{Wel00}
\by J.-Y.~Welschinger
\paper Real $J$-curves with deep nests on ruled surfaces
\inbook Geometry and topology. Part~5
\serial Zap. Nauchn. Sem. POMI
\yr 2000
\vol 267
\pages 88--118
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1267}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1809818}
\zmath{https://zbmath.org/?q=an:1027.14032}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2003
\vol 113
\issue 6
\pages 777--794
\crossref{https://doi.org/10.1023/A:1021227116716}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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