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Results tagged with schubert-varieties
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user 297
8
votes
Accepted
May Schubert cell intersection with opposite big cell polynomial count?
Yes, this is polynomial point count. An intersection of a Bruhat cell and an opposite Bruhat cell is called a "Richardson variety", and Richardson varieties come with decompositions known as Deodhar d …
- 156k
3
votes
Accepted
Looking for a canonical (matroid polytope) subdivision of the hypersimplex
The uniform matroid itself is a Schubert matroid, so the trivial subdivision where we don't subdivide at all meets this criterion.
There is no way we can use all the Schubert matroids. Let $M$ be the …
- 156k
4
votes
Do Richardson varieties have rational singularities in arbitrary characteristic?
Allen Knutson, Thomas Lam and I prove this in an Appendix we have recently added to our paper Projections of Richardson Varieties. Many thanks to Michel Brion and Shrawan Kumar for helping us by e-mai …
- 156k
6
votes
Richardson varieties over finite fields
This is both well known and complicated. The number of points on a Richardson variety over $\mathbb{F}\_q$ is given by the R-polynomials of Kazhdan and Lusztig. These are not the more famous Kazhdan-L …
- 156k