Mixed Hodge modules and mixed twistor modules

TL;DR

This paper clarifies fundamental differences between mixed Hodge modules and mixed twistor modules, focusing on their distinct weight systems and behaviors of the nearby cycle functor, which have been previously unclear.

Contribution

It explicitly explains key differences between the theories of mixed Hodge modules and mixed twistor modules, especially regarding their weight systems and nearby cycle functor.

Findings

Clarification of the differences in weight systems

Analysis of the nearby cycle functor behavior

Explicit comparison of the two theories

Abstract

We explain some fundamental differences between the theories of mixed Hodge modules and mixed twistor modules (including the difference in weight system on the nearby cycle functor) which do not seem to be clarified explicitly in the literature.