On the Classification of K3-Surfaces with Nine Cusps
| dc.creator | Barth, W. | |
| dc.date | 1998-05-19 | |
| dc.date.accessioned | 2026-07-07T05:24:47Z | |
| dc.date.available | 2026-07-07T05:24:47Z | |
| dc.description | By a K3-surface with nine cusps I mean a compact complex surface with nine isolated double points $A_2$, but otherwise smooth, such that its minimal desingularisation is a K3-surface. In an earlier paper I showd that each such surface is a quotient of a complex torus by a cyclic group of order three. Here I try to classify these $K3$-surfaces, using the period map for complex tori. In particular I show: A $K3$-surface with nine cusps carries polarizations only of degrees 0 or 2 modulo 6. This implies in particular that there is no quartic surface in projective three-space with nine cusps. (T. Urabe pointed out to me how to deduce this from a theorem of Nikulin.) In an appendix I give explicit equations of quartic surfaces in three-space with eight cusps. | |
| dc.identifier | https://arxiv.org/abs/math/9805082 | |
| dc.identifier | http://arxiv.org/abs/math/9805082 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/76939 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J28, 14J15 | |
| dc.title | On the Classification of K3-Surfaces with Nine Cusps | |
| dc.type | text |