Schubert varieties are classical objects of study in algebraic
geometry; their study often reduces to easy-to-state combinatorial
Gorensteinness is a well-known measure of the "pathology" of the singularities of an algebraic variety. Gorensteinness is a condition that
is logically weaker than smoothness but stronger than Cohen-Macaulayness.
We present a non-recursive, combinatorial characterization of which Schubert varieties in the flag variety are Gorenstein. Our answer is in
terms of generalized permutation pattern avoidance conditions.
I'll explain the algebraic geometric and representation (Borel-Weil) theoretic applications of this work. I will also describe
further combinatorial questions.
This is a joint project with Alexander Woo, see math.AG/0409490.