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Hodge Numbers from Picard-Fuchs Equations
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Hodge Numbers from Picard-Fuchs Equations
Інший ID:
2010 Mathematics Subject Classification: 14D07; 14D05; 14J32
DOI:10.3842/SIGMA.2017.045
DOI:10.3842/SIGMA.2017.045
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
476
Завантажень:
231
Анотація:
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.
