Hodge Numbers from Picard-Fuchs Equations
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-Möller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute th...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148559 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Hodge Numbers from Picard-Fuchs Equations / C.F. Doran, A. Harder, A. Thompson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 31 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710355738755072 |
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| author | Doran, C.F. Harder, A. Thompson, A. |
| author_facet | Doran, C.F. Harder, A. Thompson, A. |
| citation_txt | Hodge Numbers from Picard-Fuchs Equations / C.F. Doran, A. Harder, A. Thompson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 31 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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-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.
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| first_indexed | 2025-12-07T17:24:16Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148559 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:24:16Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Doran, C.F. Harder, A. Thompson, A. 2019-02-18T15:44:19Z 2019-02-18T15:44:19Z 2017 Hodge Numbers from Picard-Fuchs Equations / C.F. Doran, A. Harder, A. Thompson // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 31 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14D07; 14D05; 14J32 DOI:10.3842/SIGMA.2017.045 https://nasplib.isofts.kiev.ua/handle/123456789/148559 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-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. This paper is a contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko
 Yui. The full collection is available at http://www.emis.de/journals/SIGMA/modular-forms.html.
 C.F. Doran (University of Alberta) was supported by the Natural Sciences and Engineering
 Research Council of Canada, the Pacific Institute for the Mathematical Sciences, and the Visiting
 Campobassi Professorship at the University of Maryland.
 A. Harder (University of Miami) was partially supported by the Simons Collaboration Grant
 in Homological Mirror Symmetry.
 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Hodge Numbers from Picard-Fuchs Equations Article published earlier |
| spellingShingle | Hodge Numbers from Picard-Fuchs Equations Doran, C.F. Harder, A. Thompson, A. |
| title | Hodge Numbers from Picard-Fuchs Equations |
| title_full | Hodge Numbers from Picard-Fuchs Equations |
| title_fullStr | Hodge Numbers from Picard-Fuchs Equations |
| title_full_unstemmed | Hodge Numbers from Picard-Fuchs Equations |
| title_short | Hodge Numbers from Picard-Fuchs Equations |
| title_sort | hodge numbers from picard-fuchs equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148559 |
| work_keys_str_mv | AT dorancf hodgenumbersfrompicardfuchsequations AT hardera hodgenumbersfrompicardfuchsequations AT thompsona hodgenumbersfrompicardfuchsequations |