A new M-curve of eighth degree
The problem of isotopy classification of nonsingular planar projective real algebraic curves, which occurs in the first part of Hilbert's 16th problem, is solved for curves of degree not larger than 7 [see \textit{O. Ya. Viro}, Sov. Math., Dokl. 22, 566-570 (1980); translation from Dokl. Akad. Nauk SSSR 254, 1306-1310 (1980; Zbl 0481.14009)]. We construct an M-curve of degree \( 8\) of a new isotopy type, consisting of 19 ovals, lying outside one another, and three more ovals outside one another, each of which is encircled by 5 ovals of these 19 (type \(4\amalg 3<5>\) in the notation of the paper cited above). This is the last three-nested M-curve of degree \( 8.\) The total number of realized types of M-curves of degree \( 8\) amounted to 59.
scientific article; zbMATH DE number 4114797
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