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Degeneration of Schubert varieties of \(\mathrm{SL}_n/B\) to toric varieties. (English) Zbl 1017.14019

The authors show that certain Schubert varieties in \(\mathrm{SL}(n)/B\) degenerate to toric varieties. The main idea used in this article is to relate such a Schubert variety to a distributive lattice and then to use standard monomial basis in the same spirit as Gonciulea-Laskshmibai’s proof of degeneration of a Schubert variety in a minuscule \(G/P\) to a toric variety [see N. Gonciulea and V. Lakshmibai, Transform Groups 1, No. 3, 215–248 (1996; Zbl 0909.14028)].

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
06D05 Structure and representation theory of distributive lattices

Citations:

Zbl 0909.14028
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References:

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