Name
Abstract | ||
|---|---|---|
Given a parameterization phi of a rational plane curve C, we study some invariants of C via phi. 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 phi, the dual curve of C, and its singular points. Then, by analyzing the pull-backs of the global differential forms via phi, 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. |
Year | DOI | Venue |
|---|---|---|
2020 | 10.1090/mcom/3495 | MATHEMATICS OF COMPUTATION |
Field | DocType | Volume |
Dual curve,Parametrization,Mathematical analysis,Discriminant,Differential form,Canonical map,Hilbert series and Hilbert polynomial,Invariant (mathematics),Plane curve,Mathematics | Journal | 89 |
Issue | ISSN | Citations |
323 | 0025-5718 | 0 |
PageRank | References | Authors |
0.34 | 2 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Laurent Busé | 1 | 131 | 14.74 |
| A. Dimca | 2 | 11 | 2.37 |
| Gabriel Sticlaru | 3 | 0 | 1.01 |