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M-curves of degree 10. (English) Zbl 0547.14030

Translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 122, 146-161 (Russian) (1982; Zbl 0509.14052).

MSC:

14N10 Enumerative problems (combinatorial problems) in algebraic geometry
14Pxx Real algebraic and real-analytic geometry
14H45 Special algebraic curves and curves of low genus
14N05 Projective techniques in algebraic geometry
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References:

[1] A. Harnack, ?Über die Vieltheiligkeit der ebenen algebraischen Kurven,? Math. Ann.,10, 189?199 (1876). · JFM 08.0317.04 · doi:10.1007/BF01442458
[2] D. A. Gudkov, ?Topology of real projective algebraic varieties,? Usp. Mat. Nauk,29, No. 4, 3?79 (1974). · Zbl 0316.14018
[3] O. Ya. Viro, ?Curves of degree 7, curves of degree 8, and Ragsdale’s conjecture,? Dokl. Akad. Nauk SSSR,254, No. 6, 1306?1310 (1980).
[4] D. Hilbert, ?Mathematische Probleme,? Arch. Math. Phys.,3, No. 1, 213?237 (1901).
[5] V. A. Rokhlin, ?Complex topological characteristics of real algebraic curves,? Usp. Mat. Nauk,33, No. 5, 77?89 (1978). · Zbl 0437.14013
[6] G. M. Polotovskii, ?Problem of topological classification of the disposition of ovals of nonsingular algebraic curves in the projective plane,? in: Methods of the Qualitative Theory of Differential Equations [in Russian], Vol. 1, Gorki (1975), pp. 101?128.
[7] A. B. Korchagin, ?New possibilities in Brusotti’s method for constructing M-curves of orders ?8,? in: Methods of the Qualitative Theory of Differential Equations [in Russian], Vol. 2, Gorki (1978), pp. 149?159.
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