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Projective cones and \(M\)-quintics generic with respect to a maximally intersecting pair of ovals. (English. Russian original) Zbl 0998.14025
Math. Notes 65, No. 4, 528-532 (1999); translation from Mat. Zametki 65, No. 4, 632-636 (1999).
From the paper: The present paper continues the study of real plane decomposable curves of degree 7 started in the following papers: G. M. Polotovskij [in: Real algebraic geometry, Proc. Conf., Rennes 1991, Lect. Notes Math. 1524, 52-74 (1992; Zbl 0789.14028) and in: Real algebraic geometry and ordered structures, AMS Spec. Sess. Baton Rouge 1996, Contemp. Math. 253, 219-233 (2000; Zbl 0981.14029)] and S. Yu. Orevkov and G. M. Polotovskij [St. Petersburg Math. J. 11, No. 5, 837-852 (2000); translation from Algebra Anal. 11, No. 5, 166-184 (2000; Zbl 0992.14022)]; we give the isotopy classification of the curves described in the title. It happens that the case of conics and quartics is more “regular” than that of cubics and quintics: All the obstructions have similar proofs and the constructions are also similar. We follow the notation of the last cited paper.

MSC:
14P25 Topology of real algebraic varieties
57M25 Knots and links in the \(3\)-sphere (MSC2010)
14H50 Plane and space curves
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References:
[1] G. M. Polotovskii,Lecture Notes in Math.,1524, 52–74 (1992).
[2] G. M. Polotovskii, ”On the classification of decomposable 7th degree curves,”Contemp. Math. (1999) (to appear).
[3] S. Yu. Orevkov and G. M. Polotovskii, ”ProjectiveM-cubics andM-quartics generic with respect to maximally intersecting pair of ovals,”Algebra i Analiz [St. Petersburg Math. J.] (to appear).
[4] S. Yu. Orevkov, ”Link theory and oval arrangements of real algebraic curves,”Topology (to appear). · Zbl 0923.14032
[5] V. A. Rokhlin,Uspekhi Mat. Nauk [Russian Math. Surveys,33, No. 5, 77–89 (1978).
[6] T. Fidler,Isv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],46, 853–863 (1982).
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