Geradenmodelle der Möbius- und Burau-Geometrien

Let (L, K) be an arbitrary (not necessary abelian) field extension, let V be a (left) vector space over L (and therefore over the subfield K) and let μ be the set of all sub-spaces of the projective space II(V, K). Then the canonical map κ{script}: P {colon equals} V^*/K^* → U given by κ{script}: K^*a → L^*a/K^* {colon equals} {K^*(λa){divides}λ ∈ L^*{ induces a spread S in Π(V, K). Furthermore κ{script} induces a chain structure by applying κ{script} on certain subspaces of U. Our purpose is to give a synthetic description of these chain structures. For a regular Spread S, i.e. K is commutative, the chain structure is a generalization of the Burau geometries [11]. In this paper we represent the Staudt chains by Segre manifolds.