Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: High-school algebra of the theory of dicritical divisors: atypical
  fibres for special pencils and polynomials   In this work we deal with dicritical divisors, curvettes and polynomials.
These objects have been one of the main research interests of S.S. Abhyankar
during his last years. In this work we provide some elementary proofs of some
S.S. Abhyankar and I. Luengo results for dicriticals in the framework of formal
power series. Based on these ideas we give a constructive way to find the
atypical fibres of a special pencil and give bounds for its number, which are
sharper than the existing ones. Finally, we answer a question of J.
Gwo\'zdziewicz finding polynomials that reach his bound.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio