Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal affine surfaces with $\bf C^*$-actions   A classification of normal affine surfaces admitting a $\bf C^*$-action was
given in the work of Bia{\l}ynicki-Birula, Fieseler and L. Kaup, Orlik and
Wagreich, Rynes and others. We provide a simple alternative description of such
surfaces in terms of their graded rings as well as by defining equations. This
is based on a generalization of the Dolgachev-Pinkham-Demazure construction in
the case of a hyperbolic grading. As an apllication we determine the structure
of singularities, of the orbits and the divisor class groups for such surfaces.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin