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New \(M\)-curve of degree 8. (English. Russian original) Zbl 1054.14072
Funct. Anal. Appl. 36, No. 3, 247-249 (2002); translation from Funkts. Anal. Prilozh. 36, No. 3, 90-93 (2002).
From the text: A real algebraic curve in \(\mathbb{R}\mathbb{P}^2\) is called an \(M\)-curve if it has the maximal possible number \((m-1)(m-2)/2+1\) of connected components, where \(m\) is the degree of the curve. The author constructs a plane real algebraic curve of degree 8 with 22 ovals (an \(M\)-curve) realizing the isotopy type \(\langle 7\sqcup 1\langle 2 \sqcup 1\langle 11\rangle\rangle \rangle\) (for the notation, see O. Ya. Viro [Russ. Math. Surv. 41, 55–82 (1986; Zbl 0619.14015)].
MSC:
14P05 Real algebraic sets
14H45 Special algebraic curves and curves of low genus
14P25 Topology of real algebraic varieties
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