Loughborough University
Browse
sigma17-045.pdf (443.92 kB)

Hodge numbers from Picard-Fuchs equations

Download (443.92 kB)
journal contribution
posted on 2018-09-17, 12:35 authored by Charles F. Doran, Andrew Harder, Alan ThompsonAlan Thompson
Given 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 Applications

Citation

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 Sigma

Version

  • 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

2017-06-12

Publication date

2017-06-18

Notes

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

1815-0659

Language

  • en

Usage metrics

    Loughborough Publications

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC