Georgia Institute of Technology College of Sciences

Given a closed subvariety Z in a smooth complex variety X, the local cohomology sheaves with support in Z are holonomic D-modules, and thus have finite filtration with simple composition factors. We determine the D-module structure on local cohomology in the case when X is a Grassmannian and Z is a Schubert variety, including a combinatorial formula describing the composition factors and the weight filtration in the sense of mixed Hodge modules. Upon restriction to the opposite big cell, these calculations recover several previously known results concerning local cohomology with support in determinantal varieties.