Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factorial rational varieties which admit or fail to admit an elliptic
  $\mathbb{G}_m$-action   Over a field $k$, we study rational UFDs of finite transcendence degree $n$
over $k$. We classify such UFDs $B$ when $n=2$, $k$ is algebraically closed,
and $B$ admits a positive $\mathbb{Z}$-grading, showing in particular that $B$
is affine over $k$. We also consider the Russell cubic threefold over
$\mathbb{C}$, and the Asanuma threefolds over a field of positive
characterstic, showing that these threefolds admit no elliptic
$\mathbb{G}_m$-action. Finally, we show that, if $X$ is an affine $k$-variety
and $X\times\mathbb{A}^m_k\cong_k\mathbb{A}^{n+m}_k$, then
$X\cong_k\mathbb{A}^n_k$ if and only if $X$ admits an elliptic
$\mathbb{G}_m$-action.

21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg