Computing toric degenerations of flag varieties

Abstract

We compute toric degenerations arising from the tropicalization of the full flag varieties $\mathcal{F}{\ell }_4$ and $\mathcal{F}{\ell }_5$ embedded in a product of Grassmannians. For $\mathcal{F}{\ell }_4$ and $\mathcal{F}{\ell }_5$ we compare toric degenerations arising from string polytopes and the FFLV polytope with those obtained from the tropicalization of the flag varieties. We also present a general procedure to find toric degenerations in the cases where the initial ideal arising from a cone of the tropicalization of a variety is not prime.

35 pages, 6 figures

References in corpus (1)

• Toric degenerations of Gr(2,n) and Gr(3,6) via plabic graphs

Cited by in corpus (1)

• Weighted PBW degenerations and tropical flag varieties