Completion of real fans and Zariski-Riemann spaces

Abstract

Given a real fan in a real space consisting of real convex polyhedral cones, we construct a complete real fan which contains the fan, by two completely different methods. The first one is purely combinatorial and a proof of a related version was sketched earlier by Ewald. The second one is based on Nagata’s method of imbedding an abstract variety into a complete variety. For the second method, we introduce the theory of Zariski-Riemann space of a fan