Limits of Hodge structures with quasi-unipotent monodromies

TL;DR

This paper surveys the theory of limits of polarizable real Hodge structures with quasi-unipotent monodromies, focusing on the V-filtration approach by Kashiwara and Malgrange, which is less familiar.

Contribution

It introduces and explains the V-filtration method for analyzing limits of Hodge structures with quasi-unipotent monodromies, expanding understanding of this less common approach.

Findings

Clarifies the V-filtration indexed by rational numbers

Connects the V-filtration to limits of Hodge structures

Provides insights into the quasi-unipotent monodromy case

Abstract

We survey a theory of limits of polarizable variations of real Hodge structure in the quasi-unipotent monodromy case using the V-filtration of Kashiwara and Malgrange indexed by rational numbers, which does not necessarily seem familiar to many people.