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Connection between the rigid isotopy class of a fifth-order nonsingular curve in \(RP^ 2\) and its disposition with respect to a line. (English. Russian original) Zbl 0627.14039
Funct. Anal. Appl. 20, 330-332 (1986); translation from Funkts. Anal. Prilozh. 20, No. 4, 87-88 (1986).
Let a mutual location of a straight line and a non-singular curve \(K_ m^{\ell}\) of order m, containing exactly \(\ell\) ovals, be given in \(RP^ 2\). In the first non-trivial case \(m=5\), it is determined to what rigid isotopy class the curve \(K_ 5^{\ell}\) can belong. Mainly \(\ell =4\) is considered.
Reviewer: V.F.Ignatenko
MSC:
14N05 Projective techniques in algebraic geometry
14H45 Special algebraic curves and curves of low genus
14Pxx Real algebraic and real-analytic geometry
14F35 Homotopy theory and fundamental groups in algebraic geometry
Keywords:
isotopy
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