Publications of the Research Institute for Mathematical Sciences
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Published online: 2018-01-17
Free and Nearly Free Curves vs. Rational Cuspidal Plane CurvesAlexandru Dimca and Gabriel Sticlaru (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