Quiver Grassmannians and degenerate flag varieties

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.

23 pages

Cited by in corpus (7)

• Degenerate flag varieties: moment graphs and Schröder numbers
• From Submodule Categories to the Stable Auslander Algebra
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• Degenerations of Grassmannians via lattice configurations
• Desingularizations of Quiver Grassmannians for the Equioriented Cycle Quiver
• Equivariant completions of affine spaces
• Equivariant cohomology of juggling varieties in rank one