The maximum number of singular points on rational homology projective planes
| dc.creator | Hwang, Dongseon | |
| dc.creator | Keum, JongHae | |
| dc.date | 2008-01-20 | |
| dc.date | 2008-10-12 | |
| dc.date.accessioned | 2026-07-07T10:08:53Z | |
| dc.date.available | 2026-07-07T10:08:53Z | |
| dc.description | A normal projective complex surface is called a rational homology projective plane if it has the same Betti numbers with the complex projective plane $\mathbb{C}\mathbb{P}^2$. It is known that a rational homology projective plane with quotient singularities has at most 5 singular points. So far all known examples have at most 4 singular points. In this paper, we prove that a rational homology projective plane $S$ with quotient singularities such that $K_S$ is nef has at most 4 singular points except one case. The exceptional case comes from Enriques surfaces with a configuration of 9 smooth rational curves whose Dynkin diagram is of type $ 3A_1 \oplus 2A_3$. We also obtain a similar result in the differentiable case and in the symplectic case under certain assumptions which all hold in the algebraic case. | |
| dc.description | 23 pages. changed the exposition of the previous version | |
| dc.identifier | https://arxiv.org/abs/0801.3021 | |
| dc.identifier | http://arxiv.org/abs/0801.3021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171155 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14J17; 14J28 | |
| dc.title | The maximum number of singular points on rational homology projective planes | |
| dc.type | text |