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arXiv · 1106.2399

Quiver Grassmannians and degenerate flag varieties

Giovanni Cerulli Irelli·Evgeny Feigin·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 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.

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Giovanni Cerulli Irelli, Evgeny Feigin, Markus Reineke. 2011-06-13. Quiver Grassmannians and degenerate flag varieties. https://doi.org/10.2140/ant.2012.6.165

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