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Locally Finite Completions of Polyhedral Complexes

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Abstract

We develop a method for subdividing polyhedral complexes in a way that restricts the possible recession cones and allows one to work with a fixed class of polyhedron. We use these results to construct locally finite completions of rational polyhedral complexes whose recession cones lie in a fixed fan, locally finite polytopal completions of polytopal complexes, and locally finite zonotopal completions of zonotopal complexes.

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Acknowledgements

The authors are grateful to Sam Payne for his encouragement on this project and for many helpful discussions and comments. They also thank Kalina Mincheva and Jeremy Usatine for helpful conversations. Netanel Friedenberg is thankful to the Mathematical Sciences Research Institute and the organizers of the Birational Geometry and Moduli Spaces program in the Spring 2019 semester during which some of the work on this project was done (Desmond Coles was not present). This paper was also supported later by NSF DMS-2001502, and NSF DMS-2053261.

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Authors and Affiliations

  1. The University of Texas at Austin, Austin, TX, USA

    Desmond Coles

  2. Tulane University, New Orleans, LA, USA

    Netanel Friedenberg

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  1. Desmond Coles
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  2. Netanel Friedenberg
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Correspondence to Desmond Coles.

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Coles, D., Friedenberg, N. Locally Finite Completions of Polyhedral Complexes. Discrete Comput Geom (2024). https://doi.org/10.1007/s00454-024-00629-x

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  • DOI: https://doi.org/10.1007/s00454-024-00629-x

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