When do the recession cones of a polyhedral complex form a fan?
Combinatorics
2010-12-09 v2 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1008.2608,
title = {When do the recession cones of a polyhedral complex form a fan?},
author = {José Ignacio Burgos Gil and Martín Sombra},
journal= {arXiv preprint arXiv:1008.2608},
year = {2010}
}
Comments
To appear in Discrete and Computational Geometry, 8 pp