The toric geometry of triangulated polygons in euclidean space

Benjamin Howard; Christopher Manon; John Millson

doi:10.4153/CJM-2011-021-0

The toric geometry of triangulated polygons in euclidean space

Benjamin Howard, Christopher Manon, John Millson

Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

Speyer and Sturmfels associated Gröbner toric degenerations Gr ₂(C^π)^τ of Gr₂(Cⁿ) with each trivalent tree T having n leaves. These degenerations induce toric degenerations M^τ of Mr the space of n ordered, weighted (by r) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers and describe the action of the compact part of the torus as "bendings of polygons". We prove the conjecture of Foth and Hu that the toric fibers are homeomorphic to the spaces defined by Kamiyama and Yoshida.

Original language	English
Pages (from-to)	878-937
Number of pages	60
Journal	Canadian Journal of Mathematics
Volume	63
Issue number	4
DOIs	https://doi.org/10.4153/CJM-2011-021-0
State	Published - Aug 2011

Funding

Funders	Funder number
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China	0554254, 0405606, 0907446, 0703674
U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China

ASJC Scopus subject areas

General Mathematics

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title = "The toric geometry of triangulated polygons in euclidean space",

abstract = "Speyer and Sturmfels associated Gr{\"o}bner toric degenerations Gr 2(Cπ)τ of Gr2(Cn) with each trivalent tree T having n leaves. These degenerations induce toric degenerations Mτ of Mr the space of n ordered, weighted (by r) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers and describe the action of the compact part of the torus as {"}bendings of polygons{"}. We prove the conjecture of Foth and Hu that the toric fibers are homeomorphic to the spaces defined by Kamiyama and Yoshida.",

author = "Benjamin Howard and Christopher Manon and John Millson",

year = "2011",

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doi = "10.4153/CJM-2011-021-0",

language = "English",

volume = "63",

pages = "878--937",

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T1 - The toric geometry of triangulated polygons in euclidean space

AU - Howard, Benjamin

AU - Manon, Christopher

AU - Millson, John

PY - 2011/8

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AB - Speyer and Sturmfels associated Gröbner toric degenerations Gr 2(Cπ)τ of Gr2(Cn) with each trivalent tree T having n leaves. These degenerations induce toric degenerations Mτ of Mr the space of n ordered, weighted (by r) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers and describe the action of the compact part of the torus as "bendings of polygons". We prove the conjecture of Foth and Hu that the toric fibers are homeomorphic to the spaces defined by Kamiyama and Yoshida.

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The toric geometry of triangulated polygons in euclidean space

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