Holes of the Leech lattice and the projective models of K3 surfaces

TL;DR

This paper uses the theory of holes in the Leech lattice and Borcherds' method to effectively bound the number of projective models of fixed degree for specific K3 surfaces.

Contribution

It introduces a new approach combining lattice hole theory and Borcherds' method to bound projective models of K3 surfaces.

Findings

Established an effective bound for projective models of K3 surfaces

Applied lattice hole theory to algebraic geometry problems

Combined Borcherds' method with lattice theory for automorphism groups

Abstract

Using the theory of holes of the Leech lattice and Borcherds method for the computation of the automorphism group of a K3 surface, we give an effective bound for the set of isomorphism classes of projective models of fixed degree for certain K3 surfaces.