Hodge Numbers from Picard-Fuchs Equations
Algebraic Geometry
2017-06-20 v2
Abstract
Given a variation of Hodge structure over with Hodge numbers , we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-M\"oller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds.
Keywords
Cite
@article{arxiv.1612.09439,
title = {Hodge Numbers from Picard-Fuchs Equations},
author = {Charles F. Doran and Andrew Harder and Alan Thompson},
journal= {arXiv preprint arXiv:1612.09439},
year = {2017}
}