Positive sheaves of differentials coming from coarse moduli spaces
| dc.creator | Jabbusch, Kelly | |
| dc.creator | Kebekus, Stefan | |
| dc.date | 2009-04-16 | |
| dc.date.accessioned | 2026-07-07T13:04:57Z | |
| dc.date.available | 2026-07-07T13:04:57Z | |
| dc.description | Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base U, and suppose the family is non-isotrivial. If Y is a smooth compactification of U, such that D := Y U is a simple normal crossing divisor, then we can consider the sheaf of differentials with logarithmic poles along D. Viehweg and Zuo have shown that for some number m>0, the m-th symmetric power of this sheaf admits many sections. More precisely, the m-th symmetric power contains an invertible sheaf whose Kodaira-Iitaka dimension is at least the variation of the family. We refine this result and show that this "Viehweg-Zuo sheaf" comes from the coarse moduli space associated to the given family, at least generically. As an immediate corollary, if U is a surface, we see that the non-isotriviality assumption implies that U cannot be special in the sense of Campana. | |
| dc.identifier | https://arxiv.org/abs/0904.2445 | |
| dc.identifier | http://arxiv.org/abs/0904.2445 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/227349 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D22 | |
| dc.title | Positive sheaves of differentials coming from coarse moduli spaces | |
| dc.type | text |