English

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