Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Alternating Group of degree 6 in Geometry of the Leech Lattice and
  K3 Surfaces   The alternating group of degree 6 is located at the junction of three series
of simple non-commutative groups : simple sporadic groups, alternating groups
and simple groups of Lie type. It plays a very special role in the theory of
finite groups. We shall study its new roles both in a finite geometry of
certain pentagon in the Leech lattice and also in a complex algebraic geometry
of $K3$ surfaces.

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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: comp-gas