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A note on a quartic with a tacnode and a flexnode. (English) Zbl 0612.14023
For the curve described in the title the authors find the four points of inflexion (other than the flexnode) and demonstrate their relationship to the tacnode, the flexnode, and their associated tangents. They also show that the curve has $$class\quad 6$$ and genus $$0.$$ [The latter results are obvious, because a tacnode is equivalent to two nodes, so the curve has the equivalent of three nodes.]
Reviewer: E.J.F.Primrose

MSC:
 14H20 Singularities of curves, local rings 51N35 Questions of classical algebraic geometry
Keywords:
points of inflexion
Full Text:
References:
 [1] B. Bydžovský: Inflexní body některých rovinných kvartik. Časopis pro pěstování matematiky, roč. 88 (1963), str. 224-235. [2] J. Metelka: Poznámka k článku akademika Bohumila Bydžovského ”Inflexní body některých rovinných kvartik”. Časopis pro p\?stování matematiky, roč. 90 (1965), str. 455-457. [3] Dalibor Klucký, Jaromír Krys: Druhá poznámka k článku akademika Bohumila Bydžovského ”Inflexní body některých rovinných kvartik“. Časopis pro pěstování matematiky, roč. 92 (1967), str. 212-214. [4] Dalibor Klucký, Libuše Marková: A contribution to the iheory of tacnodal quartics. Časopis pro pěstování matematiky, roč. 110 (1985), str. 92-100. · Zbl 0587.14014 [5] Robert J. Walker: Algebraic curves. Springer-Verlag New York 1950. · Zbl 0039.37701
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