Abstract:
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.
Key words and phrases:rational cuspidal curves, Jacobian syzygy, Tjurina number, free curves, nearly free curves.