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Hodge numbers from Picard-Fuchs equations
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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 ISSN 1815-0659.
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Official URL: http://dx.doi.org/10.3842/SIGMA.2017.045
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 | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > 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: |
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Volume: | 13 | ||||||
Article Number: | 45 | ||||||
DOI: | 10.3842/SIGMA.2017.045 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
Date of first compliant deposit: | 19 June 2017 | ||||||
Date of first compliant Open Access: | 20 June 2017 | ||||||
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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