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POSITIVE SHEAVES OF DIFFERENTIALS COMING FROM COARSE MODULI SPACES
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Annales de l'Institut Fourier, ISSN 0373-0956, E-ISSN 1777-5310, Vol. 61, no 6, 2277-2290 p.Article in journal (Refereed) Published
Abstract [en]

Consider a smooth projective family of canonically polarized complex manifolds over a smooth quasi-projective complex base Y degrees, and suppose the family is non-isotrivial. If Y is a smooth compactification of Y degrees, such that D : = Y \ Y degrees 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 m > 0, the mth symmetric power of this sheaf admits many sections. More precisely, the mth 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 Y degrees is a surface, we see that the non-isotriviality assumption implies that Y degrees cannot be special in the sense of Campana.

Place, publisher, year, edition, pages
2011. Vol. 61, no 6, 2277-2290 p.
Keyword [en]
Moduli space, positivity of differentials
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-121389ISI: 000305036700003Scopus ID: 2-s2.0-84860343763OAI: oai:DiVA.org:kth-121389DiVA: diva2:618646
Note

QC 20130429

Available from: 2013-04-29 Created: 2013-04-29 Last updated: 2017-12-06Bibliographically approved

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Scopushttp://arxiv.org/abs/0904.2445

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