Publications of the Research Institute for Mathematical Sciences


Full-Text PDF (462 KB) | Metadata | Table of Contents | PRIMS summary
Volume 54, Issue 1, 2018, pp. 163–179
DOI: 10.4171/PRIMS/54-1-6

Published online: 2018-01-17

Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves

Alexandru Dimca[1] and Gabriel Sticlaru[2]

(1) Université de Nice Sophia Antipolis, France
(2) Ovidius University, Constanţa, Romania

We define a class of plane curves that are close to the free divisors in terms of the local cohomology of their Jacobian algebras and such that, conjecturally, any rational cuspidal curve $C$ is either free or belongs to this class. We prove this conjecture when the degree of $C$ is either even or a prime power, or when the group of $C$ is abelian.

Keywords: Free divisor, rational cuspidal curve, Jacobian ideal, Milnor algebra

Dimca Alexandru, Sticlaru Gabriel: Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves. Publ. Res. Inst. Math. Sci. 54 (2018), 163-179. doi: 10.4171/PRIMS/54-1-6