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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On arrangements of plane real quintics with respect to a pair of lines
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by A. B. Korchagin and G. M. Polotovskiĭ
Translated by: A. B. Korchagin
St. Petersburg Math. J. 21 (2010), 231-244
DOI: https://doi.org/10.1090/S1061-0022-10-01092-7
Published electronically: January 21, 2010

Abstract:

The arrangements of an $M$-curve of degree 5 with respect to a pair of lines in the projective plane are studied under the natural conditions of general position and maximality.
References
  • Anatoly B. Korchagin and Grigory M. Polotovskii, On arrangements of a plane real quintic curve with respect to a pair of lines, Commun. Contemp. Math. 5 (2003), no. 1, 1–24. MR 1958018, DOI 10.1142/S0219199703000926
  • G. M. Polotovskiĭ, A catalogue of $M$-splitting curves of order six, Dokl. Akad. Nauk SSSR 236 (1977), no. 3, 548–551 (Russian). MR 0460339
  • S. Yu. Orevkov, Positions of an $M$-quintic with respect to a conic that maximally intersect the odd branch of the quintic, Algebra i Analiz 19 (2007), no. 4, 174–242 (Russian); English transl., St. Petersburg Math. J. 19 (2008), no. 4, 625–674. MR 2381938, DOI 10.1090/S1061-0022-08-01014-5
  • S. Yu. Orevkov, Link theory and oval arrangements of real algebraic curves, Topology 38 (1999), no. 4, 779–810. MR 1679799, DOI 10.1016/S0040-9383(98)00021-4
  • O. Ya. Viro, Gluing of algebraic hypersurfaces, elimination of singularities, and constructions of curves, Proceedings of the International Topological Conference (Leningrad, 1982), Nauka, Leningrad, 1983, pp. 149–197. (Russian)
  • O. Ya. Viro, Gluing of plane real algebraic curves and constructions of curves of degrees $6$ and $7$, Topology (Leningrad, 1982) Lecture Notes in Math., vol. 1060, Springer, Berlin, 1984, pp. 187–200. MR 770238, DOI 10.1007/BFb0099934
  • —, Real algebraic manifolds with prescribed topological properties, Doctor’s Diss., Leningrad. Gos. Univ., Leningrad, 1983. (Russian)
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  • A. B. Korchagin and D. E. Smith, Patchworking singularities $A_\mu$ and $D_\mu$ and meanders of their smoothing, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 299 (2003), no. Geom. i Topol. 8, 193–217, 330 (English, with English and Russian summaries); English transl., J. Math. Sci. (N.Y.) 131 (2005), no. 1, 5366–5380. MR 2038262, DOI 10.1007/s10958-005-0409-3
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Bibliographic Information
  • A. B. Korchagin
  • Affiliation: Lobachevsky University, 23 Gagarin Ave., Nizhny Novgorod 603950, Russia
  • Email: korchagin@rf.unn.ru
  • G. M. Polotovskiĭ
  • Affiliation: Lobachevsky University, 23 Gagarin Ave., Nizhny Novgorod 603950, Russia
  • Email: polot@uic.nnov.ru
  • Received by editor(s): December 24, 2007
  • Published electronically: January 21, 2010
  • © Copyright 2010 American Mathematical Society
  • Journal: St. Petersburg Math. J. 21 (2010), 231-244
  • MSC (2000): Primary 14H50
  • DOI: https://doi.org/10.1090/S1061-0022-10-01092-7
  • MathSciNet review: 2549453