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 $\textrm{Gr}(2,n)$ arising from maximal cones in tropical Grassmannians and the ones coming from plabic graphs corresponding to $\textrm{Gr}(2,n)$. We show that a similar statement does not hold for $\textrm{Gr}(3,6)$.

19 pages