Weighted PBW degenerations and tropical flag varieties

X. Fang, E. Feigin, G. Fourier, I. Makhlin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We study algebraic, combinatorial and geometric aspects of weighted Poincaré-Birkhoff-Witt (PBW)-type 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.

Original languageEnglish
Article number1850016
JournalCommunications in Contemporary Mathematics
Issue number1
StatePublished - 1 Feb 2019
Externally publishedYes


FundersFunder number
Max Planck Institute for MathematicsRSF-DFG 16-41-01013


    • Flag varieties
    • degenerations
    • tropicalization


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