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math.AG2026
Microlocal Bernstein--Sato polynomials on singular ambient varieties
Bradley Dirks, Michael Perlman
We introduce the microlocal Bernstein--Sato polynomial of a function on a possibly singular ambient variety, extending the theory of Saito. We show that, contrary to the smooth amb…
math.AG2024
Local cohomology with support in Schubert varieties
Michael Perlman
This paper is concerned with local cohomology sheaves on generalized flag varieties supported in closed Schubert varieties, which carry natural structures as (mixed Hodge) D-module…
math.AG2023
Equivariant D-modules on 2x2xn hypermatrices
András C. Lőrincz, Michael Perlman
We study D-modules and related invariants on the space of 2 x 2 x n hypermatrices for n >= 3, which has finitely many orbits under the action of G = GL_2 x GL_2 x GL_n. We describe…