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2012 Quiver Grassmannians and degenerate flag varieties
Giovanni Cerulli Irelli, Evgeny Feigin, Markus Reineke
Algebra Number Theory 6(1): 165-194 (2012). DOI: 10.2140/ant.2012.6.165


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.


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Giovanni Cerulli Irelli. Evgeny Feigin. Markus Reineke. "Quiver Grassmannians and degenerate flag varieties." Algebra Number Theory 6 (1) 165 - 194, 2012.


Received: 16 June 2011; Revised: 18 July 2011; Accepted: 14 August 2011; Published: 2012
First available in Project Euclid: 20 December 2017

zbMATH: 1282.14083
MathSciNet: MR2950163
Digital Object Identifier: 10.2140/ant.2012.6.165

Primary: 14M15
Secondary: 16G20

Rights: Copyright © 2012 Mathematical Sciences Publishers


Vol.6 • No. 1 • 2012
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