The toric geometry of triangulated polygons in euclidean space

Benjamin Howard, Christopher Manon, John Millson

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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.

Original languageEnglish
Pages (from-to)878-937
Number of pages60
JournalCanadian Journal of Mathematics
Issue number4
StatePublished - Aug 2011

ASJC Scopus subject areas

  • General Mathematics


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