COTANGENT BUNDLES OF PARTIAL FLAG VARIETIES AND CONORMAL VARIETIES OF THEIR SCHUBERT DIVISORS
Let P be a parabolic subgroup in G = SLn(k), for k an algebraically closed field. We show that there is a G-stable closed subvariety of an affine Schubert variety in an affine partial flag variety which is a natural compactification of the cotangent bundle T*G/P. Restricting this identification to the conormal variety N*X(w) of a Schubert divisor X(w) in G/P, we show that there is a compactification of N*X(w) as an affine Schubert variety. It follows that N*X(w) is normal, Cohen–Macaulay, and Frobenius split.
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