Base spaces of non-isotrivial families of smooth minimal models

dc.creatorViehweg, Eckart
dc.creatorZuo, Kang
dc.date2001-03-20
dc.date2002-07-26
dc.date.accessioned2026-07-07T04:40:41Z
dc.date.available2026-07-07T04:40:41Z
dc.descriptionLet 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.description43 pages, Latex, final version with some new applications
dc.identifierhttps://arxiv.org/abs/math/0103122
dc.identifierhttp://arxiv.org/abs/math/0103122
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61109
dc.subjectAlgebraic Geometry
dc.subjectComplex Variables
dc.subject14D06 (Primary) 14D22, 14J15 (Secondary)
dc.titleBase spaces of non-isotrivial families of smooth minimal models
dc.typetext

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