Toric degenerations of Gr(2; n) and Gr(3; 6) via plabic graphs

Lara Bossinger; Xin  Fang; Ghislain  Fourier; Milena Hering; Martina Lanini

doi:10.1007/s00026-018-0395-z

Toric degenerations of Gr(2; n) and Gr(3; 6) via plabic graphs

Lara Bossinger, Xin Fang, Ghislain Fourier, Milena Hering, Martina Lanini

School of Mathematics

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

Abstract

We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2,n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to Gr(2,n). We show that a similar statement does not hold for Gr(3,6).

Original language	English
Pages (from-to)	491-512
Journal	Annals of Combinatorics
Volume	22
Early online date	16 Jul 2018
DOIs	https://doi.org/10.1007/s00026-018-0395-z
Publication status	Published - 30 Sept 2018

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10.1007/s00026-018-0395-z

tree_and_plabic_07032018Accepted author manuscript, 433 KB

https://arxiv.org/abs/1612.03838

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title = "Toric degenerations of Gr(2; n) and Gr(3; 6) via plabic graphs",

abstract = "We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2,n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to Gr(2,n). We show that a similar statement does not hold for Gr(3,6).",

author = "Lara Bossinger and Xin Fang and Ghislain Fourier and Milena Hering and Martina Lanini",

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AU - Bossinger, Lara

AU - Fang, Xin

AU - Fourier, Ghislain

AU - Hering, Milena

AU - Lanini, Martina

PY - 2018/9/30

Y1 - 2018/9/30

N2 - We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2,n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to Gr(2,n). We show that a similar statement does not hold for Gr(3,6).

AB - We establish an explicit bijection between the toric degenerations of the Grassmannian Gr(2,n) arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to Gr(2,n). We show that a similar statement does not hold for Gr(3,6).

U2 - 10.1007/s00026-018-0395-z

DO - 10.1007/s00026-018-0395-z

M3 - Article

SN - 0218-0006

VL - 22

SP - 491

EP - 512

JO - Annals of Combinatorics

JF - Annals of Combinatorics

ER -

Toric degenerations of Gr(2; n) and Gr(3; 6) via plabic graphs

Abstract

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