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

2010/08/16 by José Ignacio Burgos Gil, Martı́n Sombra, Gil, José Ignacio Burgos +1 · 2 citations
Computer Science · Mathematics · #14L32 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Primary 52B99 #Secondary 52B20

paper · pdf · doi:10.48550/arxiv.1008.2608

openalex publication_date 2010/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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