Weighted PBW degenerations and tropical flag varieties

Fang, Xin; Feigin, Evgeny; Fourier, Ghislain; Makhlin, Igor

doi:10.1142/S0219199718500165

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Weighted PBW degenerations and tropical flag varieties

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Makhlin, Igor
Max Planck Institute for Mathematics, Max Planck Society;

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http://dx.doi.org/10.1142/S0219199718500165
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arXiv:1711.00751.pdf
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Citation

Fang, X., Feigin, E., Fourier, G., & Makhlin, I. (2019). Weighted PBW degenerations and tropical flag varieties. Communications in Contemporary Mathematics, 21(1): 1850016. doi:10.1142/S0219199718500165.

Cite as: https://hdl.handle.net/21.11116/0000-0004-6848-7

Abstract

We study algebraic, combinatorial and geometric aspects of weighted 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.