Schubert varieties and representations of Dynkin quivers

Grzegorz Bobiński; Grzegorz Zwara

Colloquium Mathematicae (2002)

  • Volume: 94, Issue: 2, page 285-309
  • ISSN: 0010-1354

Abstract

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We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that the orbit closures in representation varieties of Dynkin quivers of type 𝔻 are normal and Cohen-Macaulay varieties.

How to cite

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Grzegorz Bobiński, and Grzegorz Zwara. "Schubert varieties and representations of Dynkin quivers." Colloquium Mathematicae 94.2 (2002): 285-309. <http://eudml.org/doc/284883>.

@article{GrzegorzBobiński2002,
abstract = {We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that the orbit closures in representation varieties of Dynkin quivers of type 𝔻 are normal and Cohen-Macaulay varieties.},
author = {Grzegorz Bobiński, Grzegorz Zwara},
journal = {Colloquium Mathematicae},
keywords = {singularities of Schubert varieties; flag varieties; Dynkin quivers; Cohen-Macaulay varieties},
language = {eng},
number = {2},
pages = {285-309},
title = {Schubert varieties and representations of Dynkin quivers},
url = {http://eudml.org/doc/284883},
volume = {94},
year = {2002},
}

TY - JOUR
AU - Grzegorz Bobiński
AU - Grzegorz Zwara
TI - Schubert varieties and representations of Dynkin quivers
JO - Colloquium Mathematicae
PY - 2002
VL - 94
IS - 2
SP - 285
EP - 309
AB - We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that the orbit closures in representation varieties of Dynkin quivers of type 𝔻 are normal and Cohen-Macaulay varieties.
LA - eng
KW - singularities of Schubert varieties; flag varieties; Dynkin quivers; Cohen-Macaulay varieties
UR - http://eudml.org/doc/284883
ER -

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