Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectra of quadratic vector fields on $\mathbb{C}^2$: The missing
  relation   Consider a quadratic vector field on $\mathbb{C}^2$ having an invariant line
at infinity and isolated singularities only. We define the extended spectra of
singularities to be the collection of the spectra of the linearization matrices
of each of the singular points over the affine part, together with all the
characteristic numbers (i.e. Camacho-Sad indices) at infinity. This collection
consists of 11 complex numbers, and is invariant under affine equivalence of
vector fields.
  In this paper we describe all polynomial relations among these numbers. There
are 5 independent polynomial relations; four of them follow from the
Euler-Jacobi, the Baum-Bott and the Camacho-Sad index theorems, and are well
known. The fifth relation was, until now, completely unknown. We provide an
explicit formula for the missing 5th relation, discuss it's meaning and prove
that it cannot be formulated as an index theorem.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin