On positions of a~real plane quintic relative to a~couple of lines
Algebra i analiz, Tome 21 (2009) no. 2, pp. 92-112.

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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.
Keywords: plane real algebraic curve, splitting algebraic curve, topological classification.
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A. B. Korchagin; G. M. Polotovskii. On positions of a~real plane quintic relative to a~couple of lines. Algebra i analiz, Tome 21 (2009) no. 2, pp. 92-112. http://geodesic.mathdoc.fr/item/AA_2009_21_2_a3/

[1] Korchagin A. B., Polotovskii G. M., “On arrangements of a plane real quintic curve with respect to a pair of lines”, Commun. Contemp. Math., 5:1 (2003), 1–24 | DOI | MR | Zbl

[2] Polotovskii G. M., “Katalog $M$-raspadayuschikhsya krivykh 6-go poryadka”, Dokl. AN SSSR, 236:3 (1977), 548–551 | MR | Zbl

[3] Orevkov S. Yu., “Raspolozheniya $M$-kvintiki otnositelno koniki, maksimalno peresekayuschei ee nechetnuyu vetv”, Algebra i analiz, 19:4 (2007), 174–242 | MR

[4] Orevkov S. Yu., “Link theory and oval arrangements of real algebraic curves”, Topology, 38:4 (1999), 779–810 | DOI | MR | Zbl

[5] Viro O. Ya., “Skleivanie algebraicheskikh giperpoverkhnostei, ustraneniya osobennostei i postroeniya krivykh”, Trudy Leningradskoi mezhdunarodnoi topologicheskoi konferentsii (Leningrad, 1982), Nauka, L., 1983, 149–197

[6] Viro O. Ya., “Gluing of plane real algebraic curves and constructions of curves of degrees 6 and 7”, Topology (Leningrad, 1982), Lecture Notes in Math., 1060, Springer, Berlin, 1984, 187–200 | MR

[7] Viro O. Ya., Veschestvennye algebraicheskie mnogoobraziya s predpisannymi topologicheskimi svoistvami, Dis. $\dots$ dokt. fiz.-mat. nauk, LGU, L., 1983

[8] Korchagin A. B., “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, 173, Amer. Math. Soc., Providence, RI, 1996, 141–155 | MR | Zbl

[9] Korchagin A. B., Smith D. E., “Patchworking singularities $A_\mu$ and $D_\mu$ and meanders of their smoothing”, Zap. nauch. semin. POMI, 299, POMI, SPb., 2003, 193–217 | MR