An algorithm to compute automorphism groups of K3 surfaces and an application to singular K3 surfaces

2013/04/28 by Shimada, Ichiro · 1 citation
#14J28 #14J50 #14Q10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1304.7427

Abstract

Let X be a complex algebraic K3 surface or a supersingular K3 surface in odd characteristic. We present an algorithm by which, under certain assumptions on X, we can calculate a finite set of generators of the image of the natural homomorphism from the automorphism group of X to the orthogonal group of the Néron-Severi lattice of X. We then apply this algorithm to certain complex K3 surfaces, among which are singular K3 surfaces whose transcendental lattices are of small discriminants.

Cited by

• Virtually abelian symmetry groups of hyperbolic lattices

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