Geometric polarized log Hodge structures for semistable families

TL;DR

This paper demonstrates that projective semistable morphisms of fs log analytic spaces naturally produce polarized log Hodge structures, establishing a canonical connection between these geometric objects.

Contribution

It introduces a canonical method to obtain polarized log Hodge structures from semistable morphisms of fs log analytic spaces, advancing the understanding of their geometric and Hodge-theoretic properties.

Findings

Semistable morphisms induce polarized log Hodge structures

Canonical construction of Hodge structures from log spaces

Enhances understanding of log geometric Hodge theory

Abstract

We prove that a projective semistable morphism of fs log analytic spaces yields polarized log Hodge structures in the canonical way.