Minuscule and cominuscule G/P

In this chapter we present the results for the minuscule and cominuscule G/P. We first present the results of Zelevinsky ([ 157 ]) and SankaranVanchinathan ([ 143 , 144 ]) on small resolutions for Schubert varieties in the minuscule and cominuscule cases. We then present the results of Brion and Polo (cf. [ 30 ])on the tangent space to Schubert varieties in the minuscule and cominuscule cases. The results of Lakshmibai—Weyman (cf. [ 112 ]) on the irreducible components of the singular loci of Schubert varieties as well as recursive formulae for the multiplicity and the Hilbert polynomial at a singular point are then presented. We have also included two closed formulas due to Kreiman—Lakshmibai ([ 89 ]), Rosenthal—Zelevinsky [ 142 ] for the multiplicity at a singular point for Schubert varieties in the Grassmannian. We have also included a closed formula for the Hilbert polynomial at a singular point due to Kreiman—Lakshmibai ([ 89 ]). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.