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A new affine \(M\)-sextic. II. (English. Russian original) Zbl 0933.14039
Russ. Math. Surv. 53, No. 5, 1099-1101 (1998); translation from Usp. Mat. Nauk. 53, No. 5, 243-244 (1998).
[For part I see Funct. Anal. Appl. 32, No. 2, 141-143 (1998); translation from Funkts. Anal. Prilozh, 32, No. 2, 91-94 (1998; Zbl 0932.14035).]
From the text: An affine real-valued algebraic curve is called an affine \(M\)-curve if it has the maximum possible number of connected components allowed by the Harnack inequality. In particular, an affine \(M\)-sextic has 16 connected components, 10 of which are ovals and the remaining 6 can be obtained from the 11th projectivisation oval by removing infinitely distant points. In the present note we extend the isotopic classification of affine \(M\)-sextics and present the details of a realization of the isotopy type \(A_3(0,5,5)\).
The construction is similar to the realization of \(B_2(1,8,1)\) presented in part I of this paper (loc. cit.). However, here we use a geometric argument, which makes it possible to shorten computations. The same argument can be applied to simplify the proof in part I.

14R05 Classification of affine varieties
14H50 Plane and space curves
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