Abstract
By an (abstract) Kummer variety Kd we mean the d-dimensiona1 torus Td modulo the involution ϰ ↔ — ϰ. The 2d elements in Td of order two are fixed points of the involution and therefore Kd has 2d isolated singularities (for d ≧ 3). Any simplicial decomposition of Kd must have at least as many vertices. In this paper we describe a highly symmetrical simplicial decomposition of Kd with 2d vertices such that the link of each vertex is a combinatorial real projective space ℝPd-1 with 2d—1 vertices. The automorphism group of order (d + 1)! 2d admits a natural representation in the affine group of dimension d over the field with two elements. A particular case is the classical Kummer surface with 16 nodes (d=4). In this case our 16-vertex triangulation has a close relationship with the abstract Kummer configuration 166.
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