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

arXiv comment19 pages

References in corpus (2)

• Cluster duality and mirror symmetry for Grassmannians
• Cluster Algebras of Type $D_4$, Tropical Planes, and the Positive Tropical Grassmannian

Cited by in corpus (1)

• Computing toric degenerations of flag varieties