Some remarks on limit mixed Hodge structure and spectrum

TL;DR

This paper discusses aspects of limit mixed Hodge structures and spectrum, clarifying known concepts for both specialists and beginners, and emphasizing the importance of explicit statements in the literature.

Contribution

It provides explicit remarks on limit mixed Hodge structures and spectrum that are not clearly stated in existing literature, aiding understanding for beginners.

Findings

Clarification of limit mixed Hodge structure properties

Explicit statements on spectrum in the literature

Bridging knowledge gap for beginners

Abstract

We give some remarks on limit mixed Hodge structure and spectrum. These are more or less well-known to the specialists, and do not seem to be stated explicitly in the literature. However, they do not seem to be completely trivial to the beginners, and may be worth writing down explicitly.