THE POSET OF RATIONAL CONES

Joseph Gubeladze; Mateusz Michalek

doi:10.2140/pjm.2018.292.103

THE POSET OF RATIONAL CONES

Joseph Gubeladze^*, Mateusz Michalek

^*Corresponding author for this work

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-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 language	English
Pages (from-to)	103-115
Number of pages	13
Journal	PACIFIC JOURNAL OF MATHEMATICS
Volume	292
Issue number	1
DOIs	https://doi.org/10.2140/pjm.2018.292.103
Publication status	Published - Jan 2018
MoE publication type	A1 Journal article-refereed

Keywords

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

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10.2140/pjm.2018.292.103

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AB - 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.

KW - rational cone

KW - poset of cones

KW - geometric realization of a poset

KW - TORIC VARIETIES

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DO - 10.2140/pjm.2018.292.103

M3 - Article

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JO - PACIFIC JOURNAL OF MATHEMATICS

JF - PACIFIC JOURNAL OF MATHEMATICS

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ER -

THE POSET OF RATIONAL CONES

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Keywords

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