Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant extensions of Ga-torsors over punctured surfaces   Motivated by the study of the structure of algebraic actions the additive
group on affine threefolds X, we consider a special class of such varieties
whose algebraic quotient morphisms X $\rightarrow$ X//Ga restrict to principal
homogeneous bundles over the complement of a smooth point of the quotient. We
establish basic general properties of these varieties and construct families of
examples illustrating their rich geometry. In particular, we give a complete
classification of a natural subclass consisting of threefolds X endowed with
proper Ga-actions, whose algebraic quotient morphisms $\pi$ : X $\rightarrow$
X//Ga are surjective with only isolated degenerate fibers, all isomorphic to
the affine plane A 2 when equipped with their reduced structures.

30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom