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

Abstract

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.

to appear in Acta Mathematica Vietnamica

References in corpus (4)

• Tables of Calabi--Yau equations
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• Calculations for Mirror Symmetry with D-branes
• The mirror quintic as a quintic

Cited by in corpus (4)

• Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
• Hodge Numbers from Picard-Fuchs Equations
• Threefolds Fibred by Mirror Sextic Double Planes
• On the cohomology groups of local systems over Hilbert modular varieties via Higgs bundles