W-translated Schubert divisors and transversal intersections
Tóm tắt
We study the toric degeneration of Weyl group translated Schubert divisors of a partial flag variety
$$F{\ell _{{n_1}, \ldots,{n_k};n}}$$
via Gelfand-Cetlin polytopes. We propose a conjecture that Schubert varieties of appropriate dimensions intersect transversally up to translation by Weyl group elements, and verify it in various cases, including the complex Grassmannian Gr(2, n) and the complete flag variety Fℓ1,2,3,4.
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