Reflective hyperbolic 2-elementary lattices, K3 surfaces and hyperkahler varieties

TL;DR

This paper computes Coxeter diagrams for large reflective hyperbolic lattices and explores their applications to the theory of K3 surfaces and hyperkähler varieties, advancing understanding of their geometric structures.

Contribution

It provides explicit Coxeter diagrams for large reflective hyperbolic lattices and applies these to study K3 surfaces and hyperkähler varieties, offering new insights.

Findings

Coxeter diagrams for several large reflective hyperbolic lattices

Identification of maximal parabolic subdiagrams

Applications to the geometry of K3 surfaces and hyperkähler varieties

Abstract

We compute Coxeter diagrams of several ``large'' reflective even 2-elementary hyperbolic lattices and their maximal parabolic subdiagrams, and give some applications of these results to the theory of K3 surfaces and hyperkahler varieties.