Hodge structures and differential operators

TL;DR

This paper introduces the concept of limiting mixed Hodge structures with an arithmetical perspective, connecting them to differential operators through elementary proofs.

Contribution

It provides a non-technical, elementary approach to defining and understanding limiting mixed Hodge structures via differential operators.

Findings

Established elementary proofs for properties of limiting mixed Hodge structures

Connected Hodge theory concepts with classical differential operator theory

Provided an accessible introduction to complex Hodge structures

Abstract

This text can be considered as a non-technical and arithmetically motivated introduction to the definition of the limiting mixed Hodge structure. We state several assertions in terms natural to the classical theory of ordinary differential operators and prove them using elementary arguments.