On the Hodge theory of the additive middle convolution

TL;DR

This paper investigates how Hodge data transforms under additive middle convolution for irreducible polarized complex Hodge structures on punctured complex affine lines, providing insights into their behavior.

Contribution

It offers a detailed analysis of the Hodge-theoretic effects of additive middle convolution on specific complex structures, a topic not extensively explored before.

Findings

Hodge data behavior characterized under convolution

Explicit formulas for transformations derived

Enhanced understanding of Hodge structures on punctured lines

Abstract

We compute the behaviour of Hodge data under additive middle convolution for irreducible variations of polarized complex Hodge structures on punctured complex affine lines.