Quiver Grassmannians and degenerate flag varieties
By Giovanni Cerulli Irelli, Evgeny Feigin, Markus Reineke. 2011
92 citations recorded by the source corpus.
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 the second named author. 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 proven 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 Poincare polynomials are derived.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/21f78ff3aacc1a4302d971c788b2d45b28258610
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Degenerate flag varieties of type A and C are Schubert varieties (2014, background): “2 and its proof have a nice and clean interpretation in terms of quivers, in the spirit of [1], [2] and [3].”