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

Research paper by JongHae Keum, Keiji Oguiso, De-Qi Zhang

Indexed on: 26 Nov '03Published on: 26 Nov '03Published in: Mathematics - Algebraic Geometry



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.