Hodge Numbers from Picard-Fuchs Equations


Type
Article
Change log
Authors
Doran, Charles F 
Harder, Andrew 
Abstract

Given a variation of Hodge structure over P1 with Hodge numbers (1,1,…,1), 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.

Description
Keywords
variation of Hodge structures, Calabi-Yau manifolds
Journal Title
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS
Conference Name
Journal ISSN
1815-0659
1815-0659
Volume Title
13
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Sponsorship
Engineering and Physical Sciences Research Council (EP/N03189X/1)