caa a22 4500 44583675X CHVBK 20180317145332.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0758-6 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0758-6 Families over special base manifolds and a conjecture of Campana [Elektronische Daten] [Kelly Jabbusch, Stefan Kebekus] 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 Géométriques. 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. Springer-Verlag, 2010 Jabbusch Kelly Department of Mathematics, KTH, 10044, Stockholm, Sweden aut Kebekus Stefan Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstrasse 1, 79104, Freiburg, Germany aut Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 847-878 0025-5874 269:3-4<847 2011 269 209 https://doi.org/10.1007/s00209-010-0758-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0758-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Jabbusch Kelly Department of Mathematics, KTH, 10044, Stockholm, Sweden aut NATIONALLICENCE 700 1- Kebekus Stefan Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Eckerstrasse 1, 79104, Freiburg, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 847-878 0025-5874 269:3-4<847 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer