Algebra & Number Theory

Quiver Grassmannians and degenerate flag varieties

Giovanni Cerulli Irelli, Evgeny Feigin, and Markus Reineke

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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.

Article information

Source
Algebra Number Theory Volume 6, Number 1 (2012), 165-194.

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729760

Digital Object Identifier
doi:10.2140/ant.2012.6.165

Zentralblatt MATH identifier
1282.14083

Subjects
Primary: 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]
Secondary: 16G20: Representations of quivers and partially ordered sets

Keywords
flag variety quiver grassmannian degeneration

Citation

Cerulli Irelli, Giovanni; Feigin, Evgeny; Reineke, Markus. Quiver Grassmannians and degenerate flag varieties. Algebra Number Theory 6 (2012), no. 1, 165--194. doi:10.2140/ant.2012.6.165. https://projecteuclid.org/euclid.ant/1513729760


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