Minimal triangulations of Kummer varieties
A combinatorial manifold of dimension d is a simplicial complex whose underlying set is a topological manifold such that the link of each vertex is a combinatorial \(d-1-\)sphere. If isolated singularities are admitted and the link of each vertex is a combinatorial \((d-1)-\)manifold we speak of a combinatorial pseudo-manifold. The main result is the following: For each \(d\geq 2\) there is a combinatorial pseudomanifold with \(2^ d\) vertices and \(d!2^{d-1}\) simplices of dimension d in which any two vertices are connected by an edge such that the underlying set is homeomorphic to the so-called Kummer variety \(K^ d\) of dimension d, that is, the d-dimensional torus modulo the mapping \(x\to -x.\) The automorphism group of order \((d+1)!2^ d\) acts transitively on the vertices and on the d-dimensional simplices. It admits a natural representation in the affine group of dimension d over the field with two elements.
scientific article; zbMATH DE number 4038638
scientific article