TY - JOUR
T1 - Weighted PBW degenerations and tropical flag varieties
AU - Fang, X.
AU - Feigin, E.
AU - Fourier, G.
AU - Makhlin, I.
N1 - Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/2/1
Y1 - 2019/2/1
N2 - 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.
AB - 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.
KW - Flag varieties
KW - degenerations
KW - tropicalization
UR - http://www.scopus.com/inward/record.url?scp=85046719102&partnerID=8YFLogxK
U2 - 10.1142/S0219199718500165
DO - 10.1142/S0219199718500165
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AN - SCOPUS:85046719102
SN - 0219-1997
VL - 21
JO - Communications in Contemporary Mathematics
JF - Communications in Contemporary Mathematics
IS - 1
M1 - 1850016
ER -