Limits of families of Brieskorn lattices and compactified classifying spaces

TL;DR

This paper explores the behavior of Brieskorn lattices over non-compact spaces, constructing a compact classifying space and analyzing the geometric structures and limits involved.

Contribution

It introduces a compact classifying space for regular singular Brieskorn lattices and studies the associated geometric and metric properties.

Findings

Constructed a compact classifying space for Brieskorn lattices.

Proved the pure polarized part has a natural hermitian structure.

Showed the induced metric space is complete.

Abstract

We investigate variations of Brieskorn lattices over non-compact parameter spaces, and discuss the corresponding limit objects on the boundary divisor. We study the associated variation of twistors and the corresponding limit mixed twistor structures. We construct a compact classifying space for regular singular Brieskorn lattices and prove that its pure polarized part carries a natural hermitian structure and that the induced distance makes it into a complete metric space.