Minimal triangulations of Kummer varieties
type: Item
instance of: scholarly article
title: Minimal triangulations of Kummer varieties
zbMATH Open document ID: 0637.52007
DOI: 10.1007/BF02941594
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52Bxx
Mathematics Subject Classification ID: 57N99
Mathematics Subject Classification ID: 57Q99
zbMATH DE Number: 4038638
zbMATH Keywords: combinatorial manifold
zbMATH Keywords: combinatorial pseudo-manifold
zbMATH Keywords: Kummer variety
author: Wolfgang Kühnel
reviewed by: Peter M. Gruber
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02941594
OpenAlex ID: W2089572122
description: scientific article; zbMATH DE number 4038638