Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Differential signatures of algebraic curves   In this paper, we adapt the differential signature construction to the
equivalence problem for complex plane algebraic curves under the actions of the
projective group and its subgroups. Given an action of a group $G$, a signature
map assigns to a plane algebraic curve another plane algebraic curve (a
signature curve) in such a way that two generic curves have the same signatures
if and only if they are $G$-equivalent. We prove that for any $G$-action, there
exists a pair of rational differential invariants, called classifying
invariants, that can be used to construct signatures. We derive a formula for
the degree of a signature curve in terms of the degree of the original curve,
the size of its symmetry group and some quantities depending on a choice of
classifying invariants. For the full projective group, as well as for its
affine, special affine and special Euclidean subgroups, we give explicit sets
of rational classifying invariants and derive a formula for the degree of the
signature curve of a generic curve as a quadratic function of the degree of the
original curve. We show that this generic degree is the sharp upper bound.

10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas