Einstein metrics on 5-dimensional Seifert bundles
| dc.creator | Kollár, János | |
| dc.date | 2004-08-13 | |
| dc.date.accessioned | 2026-07-07T05:11:16Z | |
| dc.date.available | 2026-07-07T05:11:16Z | |
| dc.description | The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified. These results are then used to construct positive Ricci curvature Einstein metrics on these manifolds. The proof has 4 main steps. First, the study of the Leray spectral sequence of the Seifert bundle, based on work of Orlik--Wagreich. Second, the study of log Del Pezzo surfaces. Third, the construction of Kähler--Einstein metrics on Del Pezzo orbifolds using the algebraic existence criterion of Demailly--Kollár. Fourth, the lifting of the Kähler--Einstein metric on the base of a Seifert bundle to an Einstein metric on the total space using the Kobayashi--Boyer--Galicki method. | |
| dc.identifier | https://arxiv.org/abs/math/0408184 | |
| dc.identifier | http://arxiv.org/abs/math/0408184 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72184 | |
| dc.subject | Differential Geometry | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 53C25 (primary) 14J26, 32Q20, 57S15 (secondary) | |
| dc.title | Einstein metrics on 5-dimensional Seifert bundles | |
| dc.type | text |