Hodge numbers from Picard-Fuchs equations

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...

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Bibliographic Details
Main Authors: Charles F. Doran, Andrew Harder, Alan Thompson
Format: Default Article
Published: 2017
Subjects:
Other mathematical sciences not elsewhere classified
Variation of Hodge structures
Calabi–Yau manifolds
Mathematical Sciences not elsewhere classified
Online Access:https://hdl.handle.net/2134/34898
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Summary: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.

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