Hodge theory of the middle convolution

TL;DR

This paper investigates how Hodge data transforms under tensoring with certain local systems and applies these results to local systems exhibiting G_2-monodromy, advancing understanding in Hodge theory and local system behavior.

Contribution

It provides explicit formulas for the behavior of Hodge data under tensor product and middle convolution with specific local systems, with applications to G_2-monodromy cases.

Findings

Formulas for Hodge data transformation under tensor and convolution operations

Application to local systems with G_2-monodromy

Enhanced understanding of Hodge structures in complex geometry

Abstract

We compute the behaviour of Hodge data by tensor product with a unitary rank-one local system and middle convolution by a Kummer unitary rank-one local system for an irreducible variation of polarized complex Hodge structure on a punctured complex affine line. We give applications of these formulas to local systems with G_2-monodromy.