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

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

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

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s10468-016-9634-3

Cite this

@article{98b18acbc13848428e622ce54aec24ff,

title = "Schubert Quiver Grassmannians",

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.",

keywords = "Dynkin quivers, Quiver Grassmannians, Schubert varieties",

author = "\{Cerulli Irelli\}, Giovanni and Evgeny Feigin and Markus Reineke",

note = "Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media Dordrecht.",

year = "2017",

month = feb,

day = "1",

doi = "10.1007/s10468-016-9634-3",

language = "الإنجليزيّة",

volume = "20",

pages = "147--161",

journal = "Algebras and Representation Theory",

issn = "1386-923X",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Schubert Quiver Grassmannians

AU - Cerulli Irelli, Giovanni

AU - Feigin, Evgeny

AU - Reineke, Markus

PY - 2017/2/1

Y1 - 2017/2/1

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

UR - http://www.scopus.com/inward/record.url?scp=84978069324&partnerID=8YFLogxK

U2 - 10.1007/s10468-016-9634-3

DO - 10.1007/s10468-016-9634-3

M3 - مقالة

SN - 1386-923X

VL - 20

SP - 147

EP - 161

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 1

ER -

Schubert Quiver Grassmannians

Abstract

Keywords

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this