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We use Higgs cohomology to determine the Hodge numbers of the firstintersection cohomology group of a local system V arising from the third directimage of a family of Calabi-Yau 3-folds over a smooth, quasi-projective curve.We give applications to Rhode's families of Calabi-Yau 3-folds without MUM.

Hodge numbers for the cohomology of Calabi-Yau type local systems