Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nullcone and the variety $\chi_\mathfrak{g}$ of a semisimple lie
  algebra   Let g be a semisimple Lie algebra of finite dimension. The nullcone N of g is
the set of (x, y) in g\timesg such that x and y are nilpotents and are in the
same Borel subalgebra. The main result of this paper is that N is a closed and
irreducible subvariety of g \times g whose normalization has rational
singularities and such that the normalization morphism is bijective.

5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th