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Families over special base manifolds and a conjecture of Campana
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2011 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 269, no 3-4, 847-878 p.Article in journal (Refereed) Published
Abstract [en]

Consider a smooth, projective family of canonically polarized varieties over a smooth, quasi-projective base manifold Y, all defined over the complex numbers. It has been conjectured that the family is necessarily isotrivial if Y is special in the sense of Campana. We prove the conjecture when Y is a surface or threefold. The proof uses sheaves of symmetric differentials associated to fractional boundary divisors on log canonical spaces, as introduced by Campana in his theory of Orbifoldes G,om,triques. We discuss a weak variant of the Harder-Narasimhan Filtration and prove a version of the Bogomolov-Sommese Vanishing Theorem that take the additional fractional positivity along the boundary into account. A brief, but self-contained introduction to Campana's theory is included for the reader's convenience.

Place, publisher, year, edition, pages
2011. Vol. 269, no 3-4, 847-878 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-53395DOI: 10.1007/s00209-010-0758-6ISI: 000297355500015Scopus ID: 2-s2.0-81555205686OAI: oai:DiVA.org:kth-53395DiVA: diva2:470280
Note
QC 20111228Available from: 2011-12-28 Created: 2011-12-28 Last updated: 2017-12-08Bibliographically approved

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