Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational curves and rational singularities   We study rational curves on algebraic varieties, especially on normal affine
varieties endowed with a $\C^*$-action. For varieties with an isolated
singularity, we show that the presence of sufficiently many rational curves
outside the singular point strongly affects the character of the singularity.
This provides an explanation of classical results due to H.A. Schwartz and G.H.
Halphen on polynomial solutions of the generalized Fermat equation.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph