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Schubert varieties, toric varieties and ladder determinantal varieties. (English) Zbl 0878.14033
Summary: We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of V. Lakshmibai and B. Sandhya [Proc. Indian Acad. Sci., Math. Sci. 100, No. 1, 45-52 (1990; Zbl 0714.14033)] on the components of the singular locus, for certain Schubert varieties in the flag variety.

MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
14M30 Supervarieties
14M06 Linkage
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