A new M-curve of eighth degree
type: Item
instance of: scholarly article
title: A new M-curve of eighth degree
zbMATH Open document ID: 0681.14031
DOI: 10.1007/BF01240445
published in: Mathematical Notes
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 4114797
zbMATH Keywords: M-curve of \(\deg ree\quad 8\)
zbMATH Keywords: isotopy type
author: Eugenii I. Shustin
MaRDI profile type: Publication
cites work: Q3949150
cites work: THE TOPOLOGY OF REAL PROJECTIVE ALGEBRAIC VARIETIES
cites work: Q3731751
cites work: Q5680234
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description: scientific article; zbMATH DE number 4114797