Toric degenerations of \(\mathrm{Gr}(2, n)\) and \(\mathrm{Gr}(3, 6)\) via plabic graphs. (English) Zbl 06948249

Bossinger, L.; Fang, Xin; Fourier, Ghislain; Hering, Milena; Lanini, Martina

Ann. Comb. 22, No. 3, 491-512 (2018).

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

MSC:

14M15	Grassmannians, Schubert varieties, flag manifolds
14T05	Tropical geometry (MSC2010)
14M25	Toric varieties, Newton polyhedra, Okounkov bodies
05C21	Flows in graphs

Keywords:

Grassmannians; toric varieties; tropical varieties; Groebner degenerations; plabic graphs

Software:

Macaulay2

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