A \((-86)\)-sphere in the \(K3\) surface. (English) Zbl 0889.14018
The self-intersection number of a smoothly embedded 2-sphere in a K3 surface is even and non-positive. No other restrictions on this number are known. Here it is shown that every even integer between \(-86\) and 0 is the self-intersection number of some embedded sphere in a K3 surface.
Reviewer: J.A.Hillman (Sydney)
MSC:
| 14J28 | \(K3\) surfaces and Enriques surfaces |
| 14C17 | Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry |
