Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves

  • Alexandru Dimca

    Université de Nice Sophia Antipolis, France
  • Gabriel Sticlaru

    Ovidius University, Constanţa, Romania
Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves cover
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Abstract

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 CC is either free or belongs to this class. We prove this conjecture when the degree of CC is either even or a prime power, or when the group of CC is abelian.

Cite this article

Alexandru Dimca, Gabriel Sticlaru, Free and Nearly Free Curves vs. Rational Cuspidal Plane Curves. Publ. Res. Inst. Math. Sci. 54 (2018), no. 1, pp. 163–179

DOI 10.4171/PRIMS/54-1-6