The Baily-Borel compactification of a family of orthogonal modular varieties

TL;DR

This paper investigates the Baily-Borel compactification of certain orthogonal modular varieties linked to hyperk"ahler manifolds, focusing on classifying boundary components, their relations, and combinatorial structure.

Contribution

It provides a detailed classification of boundary components and their incidence relations for a specific family of orthogonal modular varieties.

Findings

Classification of boundary components completed

Incidence relations among boundary components established

Combinatorial structure of the boundary analyzed

Abstract

We study the Baily-Borel compactification of a family of four-dimensional orthogonal modular varieties arising in connection with moduli and periods of compact hyperk\"ahler manifolds of deformation generalised Kummer type. Our main results concern the classification of boundary components, their incidence relations and combinatorics.