K3 Surfaces with Nine Cusps
alg-geom
2008-02-03 v1 Algebraic Geometry
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.
Cite
@article{arxiv.alg-geom/9709031,
title = {K3 Surfaces with Nine Cusps},
author = {W. Barth},
journal= {arXiv preprint arXiv:alg-geom/9709031},
year = {2008}
}
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