Schubert varieties and representations of Dynkin quivers

• Autorzy: Grzegorz Bobiński , Grzegorz Zwara
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16G20: Representations of quivers and partially ordered sets
• 14B05: Singularities
• 14M15: Grassmannians, Schubert varieties, flag manifolds
• 14L30: Group actions on varieties or schemes (quotients)
• 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 94
• Numer: 2
• Strony: 285-309

Daty

wydano

2002

Twórcy

autor

Grzegorz Bobiński

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

autor

Grzegorz Zwara

• Faculty of Mathematics and Computer Science, Nicholas Copernicus University, Chopina 12/18, 87-100 Toruń, Poland

Identyfikatory

DOI

10.4064/cm94-2-10