On arrangements of plane real quintics with respect to a pair of lines

Authors:
A. B. Korchagin and G. M. Polotovskiĭ

Translated by:
A. B. Korchagin

Original publication:
Algebra i Analiz, tom **21** (2009), nomer 2.

Journal:
St. Petersburg Math. J. **21** (2010), 231-244

MSC (2000):
Primary 14H50

DOI:
https://doi.org/10.1090/S1061-0022-10-01092-7

Published electronically:
January 21, 2010

MathSciNet review:
2549453

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The arrangements of an -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.

**1.**A. B. Korchagin and G. 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 (2004a:14060)****2.**G. M. Polotovskiĭ,*A catalogue of -splitting curves of order six*, Dokl. Akad. Nauk SSSR**236**(1977), no. 3, 548-551; English transl. in Soviet Math. Dokl.**18**(1977). MR**0460339 (57:333)****3.**S. Yu. Orevkov,*Arrangements of an -quintic with respect to a conic that maximally intersects its odd branch*, Algebra i Analiz**19**(2007), no. 4, 174-242; English transl., St. Petersburg Math. J.**19**(2008), no. 4, 625-674. MR**2381938 (2009d:14076)****4.**-,*Link theory and oval arrangements of real algebraic curves*, Topology**38**(1999), no. 4, 779-810. MR**1679799 (2000b:14066)****5.**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)**6.**-,*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**0770238 (87i:14029)****7.**-,*Real algebraic manifolds with prescribed topological properties*, Doctor's Diss., Leningrad. Gos. Univ., Leningrad, 1983. (Russian)**8.**A. B. Korchagin,*Smoothing of 6-fold singular points and constructions of the 9th degree M-curves*, Topology of Real Algebraic Varieties and Related Topics, Amer. Math. Soc. Transl. Ser. 2, vol. 173, Amer. Math. Soc., Providence, RI, 1996, pp. 141-155. MR**1384314 (97f:14058)****9.**A. B. Korchagin and D. E. Smith,*Patchworking singularities and and meanders of their smoothing*, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI)**299**(2003), 193-217; English transl., J. Math. Sci. (New York)**131**(2005), no. 1, 5366-5380. MR**2038262 (2004k:14110)**

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Additional 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

DOI:
https://doi.org/10.1090/S1061-0022-10-01092-7

Keywords:
Plane real algebraic curve,
splitting algebraic curve,
topological classification

Received by editor(s):
December 24, 2007

Published electronically:
January 21, 2010

Article copyright:
© Copyright 2010
American Mathematical Society