A note on boundary manifolds of arrangements

TL;DR

This paper explores the relationship between boundary manifolds of arrangements and the Lefschetz Theorem, leading to a generalized result connecting arrangement complements to their boundary manifolds.

Contribution

It establishes a new connection between the Lefschetz Theorem for arrangements and boundary manifolds, generalizing Hironaka's classical result.

Findings

Generalized Hironaka's theorem for arrangement complements

Identified a deep connection between Lefschetz Theorem and boundary manifolds

Enhanced understanding of arrangement boundary structures

Abstract

We note an intimate connection between the Lefschetz Theorem for c-arrangements, and a theorem of Hironaka relating the complement of an arrangement to its boundary manifold. This results in a generalization of Hironaka's result.