Differential Equations for Moving Hyperplane Arrangements

Abstract

We investigate Mellin integrals of products of hyperplanes, raised to an individual power each. We refer to the resulting functions as combinatorial correlators. We investigate their behavior when moving the hyperplanes individually. To encode these functions as holonomic functions in the constant terms of the hyperplanes, we aim to construct a holonomic annihilating $D$-ideal purely in terms of the hyperplane arrangement.