Schubert Quiver Grassmannians

Giovanni Cerulli Irelli; Evgeny Feigin; Markus Reineke

doi:10.1007/s10468-016-9634-3

Schubert Quiver Grassmannians

Giovanni Cerulli Irelli^*
, Evgeny Feigin
, Markus Reineke

^*Corresponding author for this work

University of Rome La Sapienza
Higher School of Economics
RAS - P.N. Lebedev Physics Institute
Ruhr University Bochum

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincaré polynomials of these quiver Grassmannians.

Original language	English
Pages (from-to)	147-161
Number of pages	15
Journal	Algebras and Representation Theory
Volume	20
Issue number	1
DOIs	https://doi.org/10.1007/s10468-016-9634-3
State	Published - 1 Feb 2017
Externally published	Yes

Keywords

Dynkin quivers
Quiver Grassmannians
Schubert varieties

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10.1007/s10468-016-9634-3

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abstract = "Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincar{\'e} polynomials of these quiver Grassmannians.",

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AU - Reineke, Markus

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N2 - Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincaré polynomials of these quiver Grassmannians.

AB - Quiver Grassmannians are projective varieties parametrizing subrepresentations of given dimension in a quiver representation. We define a class of quiver Grassmannians generalizing those which realize degenerate flag varieties. We show that each irreducible component of the quiver Grassmannians in question is isomorphic to a Schubert variety. We give an explicit description of the set of irreducible components, identify all the Schubert varieties arising, and compute the Poincaré polynomials of these quiver Grassmannians.

KW - Dynkin quivers

KW - Quiver Grassmannians

KW - Schubert varieties

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Schubert Quiver Grassmannians

Abstract

Keywords

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