Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds

Details Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds

2009-11-02

arxiv.org/abs/0911.0277v2

Mathematics

Algebraic Geometry

to appear in Acta Mathematica Vietnamica

Scientific paper

We use $L^2$-Higgs cohomology to determine the Hodge numbers of the parabolic
cohomology $H^1(\bar S, j_*\V)$, where the local system $\V$ arises from the
third primitive cohomology of family of Calabi-Yau threefolds over a curve
$\bar S$. The method gives a way to predict the presence of algebraic 2-cycles
in the total space of the family and is applied to some examples.

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