Enriques involutions on singular K3 surfaces of small discriminants

Abstract

We classify Enriques involutions on a K3 surface, up to conjugation in the automorphism group, in terms of lattice theory. We enumerate such involutions on singular K3 surfaces with transcendental lattice of discriminant smaller than or equal to 36. For 11 of these K3 surfaces, we apply Borcherds method to compute the automorphism group of the Enriques surfaces covered by them. In particular, we investigate the structure of the two most algebraic Enriques surfaces.

33 pages, 3 figures, 6 tables

References in corpus (1)

• Borcherds' method for Enriques surfaces

Cited by in corpus (7)

• Counting elliptic fibrations on K3 surfaces
• The elliptic modular surface of level 4 and its reduction modulo 3
• Enriques involutions on pencils of K3 surfaces
• Borcherds' method for Enriques surfaces
• 15-nodal quartic surfaces. Part II: The automorphism group
• Idoneal genera and K3 surfaces covering an Enriques surface
• On the number of Enriques quotients for supersingular K3 surfaces