Hodge numbers from Picard-Fuchs equations
journal contribution
posted on 2018-09-17, 12:35 authored by Charles F. Doran, Andrew Harder, Alan ThompsonAlan ThompsonGiven a variation of Hodge structure over P
1 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.
Funding
A. Thompson (University of Warwick/University of Cambridge) was supported by the Engineering and Physical Sciences Research Council programme grant Classification, Computation, and Construction: New Methods in Geometry.
History
School
- Science
Department
- Mathematical Sciences
Published in
Symmetry, Integrability and Geometry: Methods and ApplicationsCitation
DORAN, C.F., HARDER, A. and THOMPSON, A., 2017. Hodge numbers from Picard-Fuchs equations. Symmetry, Integrability and Geometry: Methods and Applications, 13: 045.Publisher
© The Authors. Published by SigmaVersion
- VoR (Version of Record)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-sa/4.0/Acceptance date
2017-06-12Publication date
2017-06-18Notes
This is an Open Access Article. It is published by Sigmaa under the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0) licence. Full details of this licence are available at: http://creativecommons.org/licenses/by-sa/4.0/eISSN
1815-0659Publisher version
Language
- en
