Middle multiplicative convolution and hypergeometric equations

TL;DR

This paper explores the behavior of Hodge invariants under middle multiplicative convolution, providing new insights and a novel proof for hypergeometric equations' invariants, bridging additive and multiplicative convolution theories.

Contribution

It explicitly relates additive and multiplicative convolutions to analyze Hodge invariants and offers a new proof for Fedorov's results on hypergeometric equations.

Findings

Explicit description of Hodge invariants via middle multiplicative convolution

A new proof of Fedorov's theorem on hypergeometric equations' invariants

Extension of convolution techniques to hypergeometric differential equations

Abstract

Using a relation due to Katz linking up additive and multiplicative convolutions, we make explicit the behaviour of some Hodge invariants by middle multiplicative convolution, following [DS13] and [Mar18a] in the additive case. Moreover, the main theorem gives a new proof of a result of Fedorov computing the Hodge invariants of hypergeometric equations.