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Toric degenerations of \(\mathrm{Gr}(2, n)\) and \(\mathrm{Gr}(3, 6)\) via plabic graphs. (English) Zbl 06948249
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
Software:
Macaulay2
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References:
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