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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
Macaulay2
Full Text:
##### References:
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