Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Freeness and invariants of rational plane curves   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.

10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph