Lens spaces as dual complexes of Log Calabi-Yau pairs

TL;DR

This paper constructs specific singular log Calabi-Yau 4-folds whose boundary dual complexes are homeomorphic to Lens spaces, explicitly realizing Lens spaces like L(3,1), L(5,1), and L(5,2).

Contribution

It introduces a method to produce singular log Calabi-Yau 4-folds with boundary dual complexes as Lens spaces, expanding understanding of their topological structures.

Findings

Constructed examples of log Calabi-Yau 4-folds with Lens space boundaries

Explicitly realized Lens spaces L(3,1), L(5,1), and L(5,2)

Connected finite cyclic group actions to boundary topology

Abstract

We demonstrate the construction of singular log Calabi-Yau $4$-folds such that the dual complex of the boundary is homeomorphic to a Lens space from a log Calabi-Yau surface with action of a finite cyclic group. We explicitly obtain the Lens spaces $L(3,1)$, $L(5,1)$, and $L(5,2)$ in this way.