Tautological systems, homogeneous spaces and the holonomic rank problem

TL;DR

This paper extends the understanding of hypergeometric systems linked to geometric structures by establishing a functorial approach to tautological systems on homogeneous spaces and solving the holonomic rank problem.

Contribution

It introduces a functorial construction for tautological systems on homogeneous spaces and fully resolves the holonomic rank problem for these systems.

Findings

Established a functorial framework for tautological systems

Solved the holonomic rank problem in full generality

Connected hypergeometric systems with mixed Hodge modules

Abstract

Many hypergeometric differential systems that arise from a geometric setting can be endowed with the structure of mixed Hodge modules. We generalize this fundamental result to the tautological systems associated to homogeneous spaces by giving a functorial construction for them. As an application, we solve the holonomic rank problem for such tautological systems in full generality.