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