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• W3105190693 abstract "We study horizontal subvarieties Z of a Griffiths period domain D. If Z is defined by algebraic equations, and if Z is also invariant under a large discrete subgroup in an appropriate sense, we prove that Z is a Hermitian symmetric domain D, embedded via a totally geodesic embedding in D. Next we discuss the case when Z is in addition of Calabi–Yau type. We classify the possible variations of Hodge structure (VHS) of Calabi–Yau type parameterized by Hermitian symmetric domains D and show that they are essentially those found by Gross and Sheng and Zuo, up to taking factors of symmetric powers and certain shift operations. In the weight 3 case, we explicitly describe the embedding Z↪D from the perspective of Griffiths transversality and relate this description to the Harish-Chandra realization of D and to the Korányi–Wolf tube domain description. There are further connections to homogeneous Legendrian varieties and the four Severi varieties of Zak." @default.
• W3105190693 created "2020-11-23" @default.
• W3105190693 creator A5020748889 @default.
• W3105190693 creator A5090815046 @default.
• W3105190693 date "2013-09-15" @default.
• W3105190693 modified "2023-10-05" @default.
• W3105190693 title "Semialgebraic horizontal subvarieties of Calabi–Yau type" @default.
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• W3105190693 doi "https://doi.org/10.1215/00127094-2348107" @default.
• W3105190693 hasPublicationYear "2013" @default.
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