For ADE types with an extremal or minuscule vertex, each opposite Schubert variety on one arm of the graph G_k has defining ideal given by a residual intersection of the linked variety on the other arm.
Residual intersections in cohen-macauley rings
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Residual Intersections and Schubert Varieties
For ADE types with an extremal or minuscule vertex, each opposite Schubert variety on one arm of the graph G_k has defining ideal given by a residual intersection of the linked variety on the other arm.