Behaviour of some Hodge invariants by middle convolution

TL;DR

This paper investigates how Hodge invariants change under middle additive convolution with Kummer modules, providing new formulas for Hodge data at infinity without scalar monodromy assumptions.

Contribution

It generalizes previous results by removing scalar monodromy constraints and offers explicit expressions for Hodge numbers and degrees after convolution.

Findings

Behavior of nearby cycle local Hodge data at infinity characterized

Explicit formulas for Hodge numbers and degrees derived

Generalization of previous results without scalar monodromy hypothesis

Abstract

Following an article of Dettweiler and Sabbah, this article studies the behaviour of various Hodge invariants by middle additive convolution with a Kummer module. The main result gives the behaviour of the nearby cycle local Hodge numerical data at infinity. We also give expressions for Hodge numbers and degrees of some Hodge bundles without making the hypothesis of scalar monodromy at infinity, which generalizes the resultsof Dettweiler and Sabbah.