Weighted PBW degenerations and tropical flag varieties

X. Fang, E. Feigin, G. Fourier, I. Makhlin
2018 Communications in Contemporary Mathematics  
We study algebraic, combinatorial and geometric aspects of weighted PBWtype degenerations of (partial) flag varieties in type A. These degenerations are labeled by degree functions lying in an explicitly defined polyhedral cone, which can be identified with a maximal cone in the tropical flag variety. Varying the degree function in the cone, we recover, for example, the classical flag variety, its abelian PBW degeneration, some of its linear degenerations and a particular toric degeneration.
doi:10.1142/s0219199718500165 fatcat:3lfs74cfifb6njaloyf4bzbgf4