Analyticity of the closures of some Hodge theoretic subspaces

TL;DR

This paper proves a general theorem establishing the analyticity of the closure of certain Hodge theoretic subspaces, including zero loci of degenerating normal functions, using moduli of log mixed Hodge structures.

Contribution

It introduces a broad theorem on the analyticity of closures of Hodge-theoretic subspaces, expanding understanding of degenerating normal functions.

Findings

Proves analyticity of closures of Hodge-theoretic subspaces.

Includes analyticity of zero loci of degenerating normal functions.

Utilizes moduli of log mixed Hodge structures for proof.

Abstract

In this paper, we prove a general theorem concerning the analyticity of the closure of a subspace defined by a family of variations of mixed Hodge structures, which includes the analyticity of the zero loci of degenerating normal functions. For the proof, we use a moduli of the valuative version of log mixed Hodge structures.