The structure of surfaces mapping to the moduli stack of canonically polarized varieties
| dc.creator | Kebekus, Stefan | |
| dc.creator | Kovacs, Sandor J. | |
| dc.date | 2007-07-13 | |
| dc.date.accessioned | 2026-07-07T08:17:37Z | |
| dc.date.available | 2026-07-07T08:17:37Z | |
| dc.description | Generalizing the well-known Shafarevich hyperbolicity conjecture, it has been conjectured by Viehweg that a quasi-projective manifold that admits a generically finite morphism to the moduli stack of canonically polarized varieties is necessarily of log general type. Given a quasi-projective surface that maps to the moduli stack, we employ extension properties of logarithmic pluri-forms to establish a strong relationship between the moduli map and the minimal model program of the surface. As a result, we can describe the fibration induced by the moduli map quite explicitly. A refined affirmative answer to Viehweg's conjecture for families over surfaces follows as a corollary. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/0707.2054 | |
| dc.identifier | http://arxiv.org/abs/0707.2054 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134155 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D20, 14D06 | |
| dc.title | The structure of surfaces mapping to the moduli stack of canonically polarized varieties | |
| dc.type | text |