TY - JOUR
T1 - Linear degenerations of flag varieties
AU - Cerulli Irelli, G.
AU - Fang, X.
AU - Feigin, E.
AU - Fourier, G.
AU - Reineke, M.
N1 - Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
PY - 2017/1/3
Y1 - 2017/1/3
N2 - Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of them are shown to be isomorphic to Schubert varieties and can be realized as highest weight orbits of partially degenerate Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study normality, cell decompositions of quiver Grassmannians are constructed in a wider context of equioriented quivers of type A.
AB - Linear degenerate flag varieties are degenerations of flag varieties as quiver Grassmannians. For type A flag varieties, we obtain characterizations of flatness, irreducibility and normality of these degenerations via rank tuples. Some of them are shown to be isomorphic to Schubert varieties and can be realized as highest weight orbits of partially degenerate Lie algebras, generalizing the corresponding results on degenerate flag varieties. To study normality, cell decompositions of quiver Grassmannians are constructed in a wider context of equioriented quivers of type A.
UR - http://www.scopus.com/inward/record.url?scp=85008235080&partnerID=8YFLogxK
U2 - 10.1007/s00209-016-1839-y
DO - 10.1007/s00209-016-1839-y
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AN - SCOPUS:85008235080
SN - 0025-5874
VL - 287
SP - 615
EP - 654
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1-2
ER -