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Abstract: A long standing open problem is to describe the singular
locus of a Schubert variety. Schubert varieties are indexed
by permutations. In 1990 Lakshmibai and Sandhya published an
elegant necessary and sufficient condition for smoothness of
a Schubert variety in terms of the associated permutation
and stated a conjectured description of the singular locus.
In this talk we will show that one direction of the conjecture
is true, namely, that the conjectured singular locus is
contained in the singular locus.
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