Abstract
We study the problem of when the collection of the recession cones of a polyhedral complex also forms 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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Burgos Gil and Sombra were partially supported by the MICINN research project MTM2009-14163-C02-01. Burgos Gil was also partially supported by the CSIC research project 2009501001.
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Burgos Gil, J.I., Sombra, M. When do the Recession Cones of a Polyhedral Complex Form a Fan?. Discrete Comput Geom 46, 789–798 (2011). https://doi.org/10.1007/s00454-010-9318-4
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DOI: https://doi.org/10.1007/s00454-010-9318-4