A Schubert variety is a specific type of geometric object in algebraic geometry, named after the mathematician Hermann Schubert. These varieties are constructed as intersections of certain linear subspaces in a projective space, often associated with a given flag of vector spaces. They play a crucial role in the study of Schubert calculus, which involves counting the number of intersections of these varieties. Schubert varieties can be used to understand the topology and geometry of Grassmannians, which are spaces that parameterize all linear subspaces of a given dimension within a larger vector space. They are important in various areas of mathematics, including representation theory and enumerative geometry.