K3 Surfaces with Nine Cusps

Abstract

By a K3-surface with nine cusps I mean a surface with nine isolated double points A_2, but otherwise smooth, such that its minimal desingularisation is a K3-surface. It is shown, that such a surface admits a cyclic triple cover branched precisely over the cusps. This parallels the theorem of Nikulin, that a K3-surface with 16 nodes is a Kummer quotient of a complex torus.

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Cited by in corpus (11)

• Kahlerian K3 surfaces and Niemeier lattices
• Degenerations of Kahlerian K3 surfaces with finite symplectic automorphism groups, II
• On K3 surface quotients of K3 or Abelian surfaces
• Cusps and Codes
• Equations of low-degree Projective Surfaces with three-divisible Sets of Cusps
• On Enriques surfaces with four cusps
• K3 surfaces with ten cusps
• Moduli of Gorenstein Q-homology projective planes
• Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds
• On quartics with three-divisible sets of cusps
• Wolf Barth (1942--2016)