Tohoku Mathematical Journal

Completion of real fans and Zariski-Riemann spaces

Günter Ewald and Masa-Nori Ishida

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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

Article information

Tohoku Math. J. (2), Volume 58, Number 2 (2006), 189-218.

First available in Project Euclid: 22 August 2006

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Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]


Ewald, Günter; Ishida, Masa-Nori. Completion of real fans and Zariski-Riemann spaces. Tohoku Math. J. (2) 58 (2006), no. 2, 189--218. doi:10.2748/tmj/1156256400.

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