K3 Surfaces with Nine Cusps

Details K3 Surfaces with Nine Cusps K3 Surfaces with Nine Cusps

1997-09-29

arxiv.org/abs/alg-geom/9709031v1

Mathematics

Algebraic Geometry

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Scientific paper

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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