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

TL;DR

This paper computes the Hodge numbers of certain cohomology groups associated with Calabi-Yau 3-fold families using Higgs cohomology, providing insights into their geometric structure.

Contribution

It introduces a method to determine Hodge numbers for local systems from Calabi-Yau families, especially those without MUM points.

Findings

Hodge numbers for the intersection cohomology are explicitly calculated.

Applications to specific Calabi-Yau 3-fold families are demonstrated.

New techniques for analyzing local systems in Calabi-Yau geometry are developed.

Abstract

We use Higgs cohomology to determine the Hodge numbers of the first intersection cohomology group of a local system V arising from the third direct image 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.