Moscow Mathematical Journal

Volume 18, Issue 4, October–December 2018 pp. 659–666.

On the Freeness of Rational Cuspidal Plane Curves

Authors: Alexandru Dimca (1) and Gabriel Sticlaru (2)
Author institution:(1) Université Côte d'Azur, CNRS, LJAD and INRIA, France
(2) Faculty of Mathematics and Informatics, Ovidius University Bd. Mamaia 124, 900527 Constanta, Romania

Summary:

We bring additional support to the conjecture saying that a rational cuspidal plane curve is either free or nearly free. This conjecture was confirmed for curves of even degree, and in this note we prove it for many odd degrees. In particular, we show that this conjecture holds for the curves of degree at most 34.

2010 Math. Subj. Class. Primary: 14H45; Secondary: 14B05, 14H50, 13D02, 32S35.

Keywords: Rational cuspidal curves, Jacobian syzygy, Tjurina number, free curves, nearly free curves.

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