Boundary combinatorics of orthogonal modular 4-folds

TL;DR

This paper investigates the combinatorial structure of boundary components and singularities in toroidal compactifications of orthogonal modular varieties, focusing on moduli spaces of algebraic deformation generalized Kummer 4-folds.

Contribution

It provides new insights into the boundary combinatorics and singularities of these compactifications, specifically for the moduli of algebraic deformation generalized Kummer 4-folds.

Findings

Characterization of boundary components

Analysis of singularities in compactifications

Applications to moduli of algebraic deformation Kummer 4-folds

Abstract

We study combinatorial problems related to the singularities and boundary components of toroidal compactifications of orthogonal modular varieties. In particular, those associated with the moduli of algebraic deformation generalised Kummer 4-folds.