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The universality theorems on the classification problem of configuration varieties and convex polytopes varieties. (English) Zbl 0667.52006
Topology and geometry, Rohlin Semin. 1984-1986, Lect. Notes Math. 1346, 527-543 (1988).
[For the entire collection see Zbl 0639.00032.]
The author presents a summary of his thesis which contains a systematic study of combinatorially defined configuration spaces, mainly their topological properties. For example, the set of all n-polytopes combinatorially equivalent to a given polytope is a configuration space which needs not be connected. Also the dual object of the combinatorial type of a hyperplane arrangement is an example. The author concentrates on point configurations in real projective 2-space having a certain oriented combinatorial type, and semi-algebraic varieties over \({\mathbb{Q}}\).
Reviewer: G.Ewald

52Bxx Polytopes and polyhedra