When do the recession cones of a polyhedral complex form a fan?

Details When do the recession cones of a polyhedral complex form a fan? When do the recession cones of a polyhedral complex form a fan?

2010-08-16

arxiv.org/abs/1008.2608v2

Mathematics

Combinatorics

To appear in Discrete and Computational Geometry, 8 pp

Scientific paper

We study the problem of when the collection of the recession cones of a polyhedral complex forms also a complex. We exhibit an example showing that this is no always the case. We also show that if the support of the given polyhedral complex satisfies a Minkowski-Weyl type condition, then the answer is positive. As a consequence, we obtain a classification theorem for proper toric schemes over a discrete valuation ring in terms of complete strongly convex rational polyhedral complexes.

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