# zbMATH — the first resource for mathematics

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
##### Keywords:
$$M$$-quintics; ovals; isotopy classification of curves
Full Text:
##### 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).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.