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Mathematische Zeitschrift

, Volume 287, Issue 1–2, pp 615–654 | Cite as

Linear degenerations of flag varieties

  • G. Cerulli Irelli
  • X. Fang
  • E. Feigin
  • G. Fourier
  • M. Reineke
Article

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.

Notes

Acknowledgements

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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • G. Cerulli Irelli
    • 1
  • X. Fang
    • 2
  • E. Feigin
    • 3
    • 4
  • G. Fourier
    • 5
  • M. Reineke
    • 6
  1. 1.Dipartimento di Matematica “G. Castelnuovo”Sapienza Universitá di RomaRomeItaly
  2. 2.Mathematical InstituteUniversity of CologneCologneGermany
  3. 3.Department of MathematicsNational Research University Higher School of EconomicsMoscowRussia
  4. 4.Skolkovo Institute of Science and TechnologySkolkovo Innovation CenterMoscowRussia
  5. 5.Institute for Algebra, Number Theory and Discrete MathematicsLeibniz University HannoverHannoverGermany
  6. 6.Faculty of MathematicsRuhr-Universität BochumBochumGermany

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