Abstract
We extend the short presentation due to [Borel '53] of the cohomology ring of a generalized flag manifold to a relatively short presentation of the cohomology of any of its Schubert varieties. Our result is stated in a root-system uniform manner by introducing the essential set of a Coxeter group element, generalizing and giving a new characterization of [Fulton '92]'s definition for permutations. Further refinements are obtained in type A.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 521-543 |
| Number of pages | 23 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 363 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2011 |
Keywords
- Bigrassmannian
- Cohomology presentation
- Essential set
- Schubert calculus
- Schubert variety