Positive sheaves of differentials coming from coarse moduli spaces

dc.creatorJabbusch, Kelly
dc.creatorKebekus, Stefan
dc.date2009-04-16
dc.date.accessioned2026-07-07T13:04:57Z
dc.date.available2026-07-07T13:04:57Z
dc.descriptionConsider 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.identifierhttps://arxiv.org/abs/0904.2445
dc.identifierhttp://arxiv.org/abs/0904.2445
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227349
dc.subjectAlgebraic Geometry
dc.subject14D22
dc.titlePositive sheaves of differentials coming from coarse moduli spaces
dc.typetext

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