The Alternating Group of degree 6 in Geometry of the Leech Lattice and K3 Surfaces

Details The Alternating Group of degree 6 in Geometry of the Leech Lattice and K3 Surfaces The Alternating Group of degree 6 in Geometry of the Leech Lattice and K3 Surfaces

2003-11-26

arxiv.org/abs/math/0311462v1

Mathematics

Algebraic Geometry

24 pages, 6 figures

Scientific paper

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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