Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Kara\'s type theorems for the multidegrees of polynomial
  automorphisms   To solve Nagata's conjecture, Shestakov-Umirbaev constructed a theory for
deciding wildness of polynomial automorphisms in three variables. Recently,
Kara\'s and others study multidegrees of polynomial automorphisms as an
application of this theory. They give various necessary conditions for triples
of positive integers to be multidegrees of tame automorphisms in three
variables. In this paper, we prove a strong theorem unifying these results
using the generalized Shestakov-Umirbaev theory.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys