Schubert variety

Summary

A Schubert variety is a subvariety of a Grassmannian or a flag variety defined by conditions on how a subspace meets a fixed flag. In a Grassmannian they are indexed by partitions that fit in a rectangle. Their classes form a basis of the cohomology ring, and computing products of these classes is Schubert calculus. Schubert varieties are usually singular, and their singularities are studied through combinatorics.