Base spaces of non-isotrivial families of smooth minimal models
| dc.creator | Viehweg, Eckart | |
| dc.creator | Zuo, Kang | |
| dc.date | 2001-03-20 | |
| dc.date | 2002-07-26 | |
| dc.date.accessioned | 2026-07-07T04:40:41Z | |
| dc.date.available | 2026-07-07T04:40:41Z | |
| dc.description | Let f: V --> U be a smooth non-isotrivial family of canonically polarized n-dimensional complex manifolds, where U is the complement of a normal crossing divisor S in a projective manifold Y. We show that some symmetric product of the sheaf of one-forms with logarithmic poles along S contains an invertible subsheaf of positive Kodaira dimension. As a corollary one finds that U can not be a complete intersection in the projective N space of codimension l < N/2, nor the complement of l general hyperplanes, for l < N. Moreover, as shown by S. Kovacs before, U can not be a projective manifold with a nef tangent bundle. If the induced morphism to the moduli scheme is generically finite, one can also exclude U to be the product of more than n curves. Moreover, the existence of the family forces the automorphism group of U to be finite. Most of those results carry over to smooth families f:V --> U, with an f-semi-ample dualizing sheaf, provided f is of maximal variation. | |
| dc.description | 43 pages, Latex, final version with some new applications | |
| dc.identifier | https://arxiv.org/abs/math/0103122 | |
| dc.identifier | http://arxiv.org/abs/math/0103122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61109 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 14D06 (Primary) 14D22, 14J15 (Secondary) | |
| dc.title | Base spaces of non-isotrivial families of smooth minimal models | |
| dc.type | text |