The Alternating Group of degree 6 in Geometry of the Leech Lattice and K3 Surfaces
JongHae Keum, Keiji Oguiso, De-Qi Zhang
Abstract
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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