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Differential Equations for Moving Hyperplane Arrangements

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arxiv 2412.09479 v2 pith:6CAF4XLY submitted 2024-12-12 math.CO math.AG

Anaëlle Pfister , Anna-Laura Sattelberger This is my paper
classification math.COmath.AG
keywords functionshyperplanesholonomichyperplaneinvestigatemovingtermsannihilating
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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.

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Cited by 1 Pith paper

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  1. Differential Space of Feynman Integrals: Annihilators and $\mathcal{D}$-module

    hep-th 2025-06 conditional novelty 6.0 of 10

    A Griffiths-Dwork based algorithm builds annihilators and D-modules for Feynman-like integrals, and in all tested cases the holonomic rank matches the twisted de Rham cohomology dimension.

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