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.

Quiver Grassmannians and degenerate flag varieties / CERULLI IRELLI, Giovanni; Feigin, Evgeny; Reineke, Markus. - In: ALGEBRA & NUMBER THEORY. - ISSN 1937-0652. - STAMPA. - 6:1(2012), pp. 165-194. [10.2140/ant.2012.6.165]

Quiver Grassmannians and degenerate flag varieties

CERULLI IRELLI, GIOVANNI;
2012

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/963928
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