Linear degenerations of flag varieties

Cerulli Irelli, G., Fang, X., Feigin, E., Fourier, G. and Reineke, M. (2017) Linear degenerations of flag varieties. Mathematische Zeitschrift, 287(1-2), pp. 615-654. (doi: 10.1007/s00209-016-1839-y)

Abstract

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.

• Item Type: Articles
• Additional Information: X.F. is supported by the Alexander von Humboldt Foundation. X.F would like to thank G.C-I. for invitation to Sapienza-Università di Roma where part of this work is carried out. G.C-I., G.F. and M.R. were partially supported by the DFG priority program 1388 “Representation Theory”, in whose context this project has been initiated. EF was supported by the RSF-DFG grant 16-41-01013. G.C.I. was also supported by the italian FIRB program “Perspectives in Lie Theory” RBFR12RA9W.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Fourier, Dr Ghislain
• Authors: Cerulli Irelli, G., Fang, X., Feigin, E., Fourier, G., and Reineke, M.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Mathematische Zeitschrift
• Publisher: Springer
• ISSN: 0025-5874
• ISSN (Online): 1432-1823
• Published Online: 03 January 2017
• Copyright Holders: Copyright © 2017 Springer-Verlag
• First Published: First published in Mathematische Zeitschrift 287(1-2):615-654
• Publisher Policy: Reproduced in accordance with the publisher copyright policy