Mathematical Research Letters

Volume 24 (2017)

Number 4

Free divisors and rational cuspidal plane curves

Pages: 1023 – 1042



Alexandru Dimca (Université Côte d’Azur, CNRS, LJAD, France)

Gabriel Sticlaru (Faculty of Mathematics and Informatics, Ovidius University, Constanta, Romania)


A characterization of freeness for plane curves in terms of the Hilbert function of the associated Milnor algebra is given as well as many new examples of rational cuspidal curves which are free.


free divisor, rational cuspidal curve, Jacobian ideal, Milnor algebra

2010 Mathematics Subject Classification

Primary 14B05, 14H45. Secondary 14C20, 14H50.

A. Dimca was partially supported by Institut Universitaire de France.

Received 29 April 2015

Accepted 13 December 2016

Published 9 November 2017