15 September 2013 Semialgebraic horizontal subvarieties of Calabi–Yau type
Robert Friedman, Radu Laza
Duke Math. J. 162(12): 2077-2148 (15 September 2013). DOI: 10.1215/00127094-2348107


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 ZD 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.


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Robert Friedman. Radu Laza. "Semialgebraic horizontal subvarieties of Calabi–Yau type." Duke Math. J. 162 (12) 2077 - 2148, 15 September 2013. https://doi.org/10.1215/00127094-2348107


Published: 15 September 2013
First available in Project Euclid: 9 September 2013

zbMATH: 06218375
MathSciNet: MR3102477
Digital Object Identifier: 10.1215/00127094-2348107

Primary: 14D07 , 32G20
Secondary: 32M15

Rights: Copyright © 2013 Duke University Press


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Vol.162 • No. 12 • 15 September 2013
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