Quiver Grassmannians and degenerate flag varieties

Giovanni Cerulli Irelli, Evgeny Feigin, Markus Reineke

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

Quiver Grassmannians are varieties parametrizing subrepresentations of a quiver representation. It is observed that certain quiver Grassmannians for type A quivers are isomorphic to the degenerate flag varieties investigated earlier by Feigin. This leads to the consideration of a class of Grassmannians of subrepresentations of the direct sum of a projective and an injective representation of a Dynkin quiver. It is proved that these are (typically singular) irreducible normal local complete intersection varieties, which admit a group action with finitely many orbits and a cellular decomposition. For type A quivers, explicit formulas for the Euler characteristic (the median Genocchi numbers) and the Poincaré polynomials are derived.

Original languageEnglish
Pages (from-to)165-194
Number of pages30
JournalAlgebra and Number Theory
Volume6
Issue number1
DOIs
Publication statusPublished - 2012
Externally publishedYes

Keywords

  • Degeneration
  • Flag variety
  • Quiver grassmannian

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