Further Geometric Properties of Schubert Varieties

In this chapter, using standard monomial basis, we prove Cohen–Macaulayness and normality for Schubert varieties; these geometric properties are proved even for the cones over Schubert varieties. We also give a characterization of arithmetically factorial Schubert varieties. The chapter also includes determination of the singular locus of a Schubert variety, and the tangent space at a singular point of a Schubert variety.