Let r < n be positive integers and further suppose r and n are coprime. We study the GIT quotient of Schubert varieties X(w) in the Grassmannian G r,n , admitting semistable points for the action of T with respect to the T -linearized line bundle L(nω r ). We give necessary and sufficient combinatorial conditions for the GIT quotient T \ \X(w) ss T (L(nω r )) to be smooth.
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