On smoothness and Gorensteinness of Schubert varieties
-- Alexander Yong

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We give an explicit combinatorial characterization of which
Schubert varieties in the flag variety are smooth;
geometrically: a Schubert variety is Gorenstein if and only if
it is Gorenstein at the generic points of the singular
locus. We also describe the canonical sheaf in terms of the
Borel-Weil construction. I'll also explain applications of this
to geometric and representation-theoretic questions.