Beiträge zur Algebra und Geometrie <BR> Contributions to Algebra and GeometryVol. 40, No. 2, pp. 309-329 (1999)

Rational 1- and 2-cuspidal Plane Curves

Torsten Fenske

Fakultät für Mathematik, Ruhr Universität Bochum, Ge. NA 2/31, Universitätsstr. 150, D-44780 Bochum, e-mail:

Abstract: We prove the existence of series of plane rational $1$- and $2$-cuspidal curves by constructing suitable Cremona transformations which transform the curves $V(xy^{d-1}-z^d )$ resp. $V(xy^{d-1}-z^d-z^{d-1}y)$ into the desired ones. Further, we obtain a complete list of existing types of rational cuspidal plane curves having one or two cusps with maximal multiplicity $m_{\rm{max}} = \deg C - 2$ resp. $m_{\rm{max}} = \deg C - 3$.

Classification (MSC91): 14H20, 14H10, 14D15, 14N05

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