Singularities of affine Schubert varieties.
Schubert varieties, toric varieties and ladder determinantal varieties
We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the 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 Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in , Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus,...
Wahl’s conjecture holds in odd characteristics for symplectic and orthogonal Grassmannians
It is shown that the proof by Mehta and Parameswaran of Wahl’s conjecture for Grassmannians in positive odd characteristics also works for symplectic and orthogonal Grassmannians.
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