Freeness and invariants of rational plane curves

Abstract : Given a parameterization φ of a rational plane curve C, we study some invariants of C via φ. We first focus on the characterization of rational cuspidal curves, in particular we establish a relation between the discriminant of the pull-back of a line via φ, the dual curve of C and its singular points. Then, by analyzing the pull-backs of the global differential forms via φ, we prove that the (nearly) freeness of a rational curve can be tested by inspecting the Hilbert function of the kernel of a canonical map. As a by product, we also show that the global Tjurina number of a rational curve can be computed directly from one of its parameterization, without relying on the computation of an equation of C.
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Contributor : Laurent Busé <>
Submitted on : Monday, April 16, 2018 - 3:12:10 PM
Last modification on : Tuesday, August 27, 2019 - 1:09:49 AM

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  • HAL Id : hal-01767751, version 1
  • ARXIV : 1804.06194

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Laurent Busé, Alexandru Dimca, Gabriel Sticlaru. Freeness and invariants of rational plane curves. 2018. ⟨hal-01767751v1⟩

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