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

2015/02/07 by Ichiro Shimada, Shimada, Ichiro
Mathematics · #Algebraic Geometry and Number Theory #Finite Group Theory Research #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1502.02099

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.

Related

• A supersingular K3 surface in characteristic 2 and the Leech lattice
• Automorphism groups in a family of K3 surfaces
• An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces
• Automorphisms of K3 surfaces, signatures, and isometries of lattices
• Neighbors and arithmetic of isogenous K3 surfaces