THE POSET OF RATIONAL CONES

Joseph Gubeladze*, Mateusz Michalek

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We introduce a natural partial order on the set Cones(d) of rational cones in R-d. The poset of normal polytopes, studied by Bruns and the authors (Discrete Comput. Geom. 56:1 (2016), 181-215), embeds into Cones(d) via the homogenization map. The order in Cones(d) is conjecturally the inclusion order. We prove this for d = 3 and show a stronger version of the connectivity of Cones(d) for all d. Topological aspects of the conjecture are also discussed.

Original languageEnglish
Pages (from-to)103-115
Number of pages13
JournalPACIFIC JOURNAL OF MATHEMATICS
Volume292
Issue number1
DOIs
Publication statusPublished - Jan 2018
MoE publication typeA1 Journal article-refereed

Keywords

  • rational cone
  • poset of cones
  • geometric realization of a poset
  • TORIC VARIETIES

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