6533b7d8fe1ef96bd126b6c5

RESEARCH PRODUCT

Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems

Stefan Müller–stachHenning Hollborn

subject

AlgebraHodge conjecturePure mathematicsMathematics::Algebraic Geometryp-adic Hodge theoryHodge theoryGroup cohomologyDe Rham cohomologyEquivariant cohomologyType (model theory)Mathematics::Symplectic GeometryHodge structureMathematics

description

We determine the Hodge numbers of the cohomology group \(H_{L^{2}}^{1}(S, \mathbb{V}) = H^{1}(\bar{S},j_{{\ast}}\mathbb{V})\) using Higgs cohomology, where the local system \(\mathbb{V}\) is induced by a family of Calabi-Yau threefolds over a smooth, quasi-projective curve S. This generalizes previous work to the case of quasi-unipotent, but not necessarily unipotent, local monodromies at infinity. We give applications to Rohde’s families of Calabi-Yau 3-folds.

https://doi.org/10.1007/978-3-319-05404-9_9