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Algebraic and Complex Geometry pp 225–240Cite as

Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 71))

Abstract

We determine the Hodge numbers of the cohomology group \(H_{L^{2}}^{1}(S, \mathbb{V}) = H^{1}(\bar{S},j_{{\ast}}\mathbb{V})\) using Higgs cohomology, where the local system \(\mathbb{V}\) is induced by a family of Calabi-Yau threefolds over a smooth, quasi-projective curve S. This generalizes previous work to the case of quasi-unipotent, but not necessarily unipotent, local monodromies at infinity. We give applications to Rohde’s families of Calabi-Yau 3-folds.

Klaus Hulek zum 60. Geburtstag gewidmet

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References

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Acknowledgements

This work builds up on [2] in an essential way, and we would like to thank P. L. del Angel, D. van Straten, and K. Zuo for the previous collaboration. We thank Xuanming Ye for several additional discussions, and the referee for some valuable improvements. This work was supported by DFG Sonderforschungsbereich/Transregio 45.

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Authors and Affiliations

  1. Mathematisches Institut der Johannes Gutenberg Universität Mainz, Staudingerweg 9, 55099, Mainz, Germany

    Henning Hollborn & Stefan Müller–Stach

Authors
  1. Henning Hollborn
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  2. Stefan Müller–Stach
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Correspondence to Stefan Müller–Stach .

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Editors and Affiliations

  1. Leibniz Universität Hannover, Hannover, Germany

    Anne Frühbis-Krüger

  2. Humboldt-University Berlin, Berlin, Germany

    Remke Nanne Kloosterman

  3. Leibniz Universität Hannover, Hannover, Germany

    Matthias Schütt

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Hollborn, H., Müller–Stach, S. (2014). Hodge Numbers for the Cohomology of Calabi-Yau Type Local Systems. In: Frühbis-Krüger, A., Kloosterman, R., Schütt, M. (eds) Algebraic and Complex Geometry. Springer Proceedings in Mathematics & Statistics, vol 71. Springer, Cham. https://doi.org/10.1007/978-3-319-05404-9_9

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