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Polarized variation of Hodge structures of Calabi–Yau type and characteristic subvarieties over bounded symmetric domains

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Abstract

In this paper, we extend the construction of the canonical polarized variation of Hodge structures over tube domain considered by Gross (Math Res Lett 1:1–9, 1994) to bounded symmetric domain and introduce a series of invariants of infinitesimal variation of Hodge structures, which we call characteristic subvarieties. We prove that the characteristic subvariety of the canonical polarized variations of Hodge structures over irreducible bounded symmetric domains are identified with the characteristic bundles defined by Mok (Ann Math 125(1):105–152, 1987). We verified the generating property of Gross for all irreducible bounded symmetric domains, which was predicted in Gross (Math Res Lett 1:1–9, 1994).

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Authors and Affiliations

  1. Department of Mathematics, East China Normal University, 200062, Shanghai, People’s Republic of China

    Mao Sheng

  2. Universität Mainz, Fachbereich 17, Mathematik, 55099, Mainz, Germany

    Kang Zuo

Authors
  1. Mao Sheng
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  2. Kang Zuo
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Correspondence to Kang Zuo.

Additional information

This work was supported by the SFB/TR 45 Periods, Moduli Spaces and Arithmetic of Algebraic Varieties of the DFG (German Research Foundation). M. Sheng is supported by a Postdoctoral Fellowship in the East China Normal University.

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Sheng, M., Zuo, K. Polarized variation of Hodge structures of Calabi–Yau type and characteristic subvarieties over bounded symmetric domains. Math. Ann. 348, 211–236 (2010). https://doi.org/10.1007/s00208-009-0378-9

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  • DOI: https://doi.org/10.1007/s00208-009-0378-9

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