On the isotriviality of families of projective manifolds over curves
| dc.creator | Viehweg, Eckart | |
| dc.creator | Zuo, Kang | |
| dc.date | 2000-02-24 | |
| dc.date | 2000-07-14 | |
| dc.date.accessioned | 2026-07-07T06:32:48Z | |
| dc.date.available | 2026-07-07T06:32:48Z | |
| dc.description | Let Y be a projective non-singular curve of genus g, X a projective manifold, both defined over the field of complex numbers, and let f:X ---> Y be a surjective morphism with general fibre F. If the Kodaira dimension of X is non-negative, and if Y is the projective line we show that f has at least 3 singular fibres. In general, for non-isotrivial morphisms f, one expects that the number of singular fibres is at least 3, if g=0, or at least 1, if g=1. Using the strong additivity of the Kodaira dimension, this is verified, if either F is of general type, or if F has a minimal model with a semi-ample canonical divisor. The corresponding result has been obtained by Migliorini and Kovacs, for families of surfaces of general type and for families of canonically polarized manifolds, and by Oguiso-Viehweg for families of elliptic surfaces. As a byproduct we obtain explicit bounds for the degree of the direct image of powers of the dualizing sheaf, generalizing those obtained by Bedulev-Viehweg for families of surfaces of general type. | |
| dc.description | 14 pages, LaTeX, more typos corrected, references updated, the arguments in sections 3 and 4 were partly reformulated | |
| dc.identifier | https://arxiv.org/abs/math/0002203 | |
| dc.identifier | http://arxiv.org/abs/math/0002203 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98983 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14D06 (Primary) 14D05, 14J10 (Secondary) | |
| dc.title | On the isotriviality of families of projective manifolds over curves | |
| dc.type | text |