From moment graphs to intersection cohomology
By Tom Braden, Robert D. MacPherson. 2000
134 citations recorded by the source corpus.
Abstract. We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our formula applies includes Schubert varieties in flag varieties and affine flag varieties. We also prove a monotonicity result on local intersection cohomology stalks.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/90dca00a6ad45b2b51d144506fcd57baad3eba93
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Discrete Mathematics and Combinatorics
- Geordie Williamson
- Alexander Yong
- Alexander Woo
- P. Fiebig
- Julianna Tymoczko
- Tom Braden
- Sara C. Billey
- Simon Riche
In Geometry and Topology
- Geordie Williamson
- Alexander Yong
- Alexander Woo
- P. Fiebig
- Julianna Tymoczko
- D. Juteau
- C. Mautner
- Tom Braden
In Mathematical Physics
- Geordie Williamson
- Alexander Yong
- P. Fiebig
- Alexander Woo
- Julianna Tymoczko
- Tom Braden
- D. Juteau
- C. Mautner
Citations in the corpus
- An upper bound on the exceptional characteristics for Lusztig's character formula (2008, background): “tion map Γ(I′,M) → Γ(I,M). 2.9. Braden-MacPherson sheaves. In this section we introduce the sheaves B(w) for w ∈ V that are of greatest interest for us. They made their first appearance in the article [BM], where they were called the canonical sheaves. The construction of B(w) is easily motivated by ”
- Parity sheaves, moment graphs and the p-smooth locus of Schubert varieties (2010, methodology): “On en déduit que l’algorithme de Braden-MacPherson peut être utilisé pour calculer les caractères des modules basculants pour les groupes algébriques.”
- Parity Sheaves (2009, background): “Similarly to case of toric varieties, in [BM01] Braden”
- Sheaves on affine Schubert varieties, modular representations and Lusztig's conjecture (2007, unknown): “It is called the canonical sheaf in [BM01] .”
- GOVERNING SINGULARITIES OF SCHUBERT VARIETIES (2006, background): “Although dimensions of local intersection cohomology groups are not in general (upper or lower) semicontinuous, a result of Irving [17] (see also [5]) shows that they behave in an upper semicontinuous manner on Schubert varieties.”
- The combinatorics of Coxeter categories (2005, background): “Let k be a field and W a vector space over k. A W-moment graph G = (V, E, ≤, l) is given by (cf. [ BMP ])”
- An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson (2005, background): “ap ρ in effect chooses a “global north” and is discussed further in the next paragraph. When X and its T-action satisfy certain conditions, for instance if the T-action induces a Whitney stratification [BM] or if the T-action is Hamiltonian [GuZ, Theorem 1.4.2], then the convention that if u is AN INT”
- Lower bounds for Kazhdan-Lusztig polynomials from patterns (2002, background): “The first inequality comes from the monotonicity of Kazhdan–Lusztig polynomials [I], [ BrM2 , Corollary 3.7].”