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2007 On the Number of Cusps of Rational Cuspidal Plane Curves
Jens Piontkowski
Experiment. Math. 16(2): 251-256 (2007).

Abstract

A cuspidal curve is a curve whose singularities are all cusps, i.e., unibranched singularities. This article describes computations that lead to the following conjecture: A rational cuspidal plane curve of degree greater than or equal to six has at most three cusps. The curves with precisely three cusps occur in three series. Assuming the Flenner--Zaidenberg rigidity conjecture, the above conjecture is verified up to degree $20$

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Jens Piontkowski. "On the Number of Cusps of Rational Cuspidal Plane Curves." Experiment. Math. 16 (2) 251 - 256, 2007.

Information

Published: 2007
First available in Project Euclid: 7 March 2008

zbMATH: 1147.14011
MathSciNet: MR2339280

Subjects:
Primary: 14H20 , 14H45 , 14H50

Keywords: cusps , plane curves , Rational curves , singularities

Rights: Copyright © 2007 A K Peters, Ltd.

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Vol.16 • No. 2 • 2007
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