Tohoku Mathematical Journal
2006
June
SECOND SERIES VOL. 58, NO. 2

Tohoku Math. J.
58 (2006), 189-218

Title COMPLETION OF REAL FANS AND ZARISKI-RIEMANN SPACES

Author Günter Ewald and Masa-Nori Ishida

(Received April 14, 2004, revised November 1, 2004)
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.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 52B20.

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