Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The automorphism group of a rigid affine variety   An irreducible algebraic variety $X$ is rigid if it admits no nontrivial
action of the additive group of the ground field. We prove that the
automorphism group $\text{Aut}(X)$ of a rigid affine variety contains a unique
maximal torus $\mathbb{T}$. If the grading on the algebra of regular functions
$\mathbb{K}[X]$ defined by the action of $\mathbb{T}$ is pointed, the group
$\text{Aut}(X)$ is a finite extension of $\mathbb{T}$. As an application, we
describe the automorphism group of a rigid trinomial affine hypersurface and
find all isomorphisms between such hypersurfaces.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
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The categories of this paper are: math-ph