Doran, Charles F., Harder, Andrew and Thompson, Alan (2017) Hodge numbers from Picard-Fuchs equations. Symmetry, Integrability and Geometry: Methods and Applications, 13 . 45. doi:10.3842/SIGMA.2017.045

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Abstract

Given a variation of Hodge structure over P1P1 with Hodge numbers (1,1,…,1)(1,1,…,1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-Möller-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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hodge theory
Journal or Publication Title:	Symmetry, Integrability and Geometry: Methods and Applications
Publisher:	Natsional'na Akademiya Nauk Ukrainy * Instytut Matematyky,National Academy of Sciences of Ukraine, Institute of Mathematics
ISSN:	1815-0659
Official Date:	18 June 2017
Dates:	Date Event 18 June 2017 Published 12 June 2017 Accepted
Date of first compliant deposit:	19 June 2017
Volume:	13
Article Number:	45
DOI:	10.3842/SIGMA.2017.045
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Open Access
Funder:	Natural Sciences and Engineering Research Council of Canada (NSERC), Pacific Institute for the Mathematical Sciences, University of Maryland at Baltimore, Simons Foundation (SF), Engineering and Physical Sciences Research Council (EPSRC)

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