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# On geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains

 dc.contributor.advisor Laza, Radu en_US dc.contributor.author Zhang, Zheng en_US dc.contributor.other Department of Mathematics. en_US dc.date.accessioned 2017-09-20T16:50:11Z dc.date.available 2017-09-20T16:50:11Z dc.date.issued 2014-12-01 en_US dc.identifier.uri http://hdl.handle.net/11401/76418 en_US dc.description 91 pg. en_US dc.description.abstract Based on the work of Gross and Sheng and Zuo, Friedman and Laza show that over every irreducible Hermitian symmetric domain there exists a canonical variation of real Hodge structure of Calabi-Yau type. The first part of the thesis concerns motivic realizations of the canonical Calabi-Yau variations over irreducible Hermitian symmetric domains of tube type. In particular, we show that certain rational descents of the canonical variations of Calabi-Yau type over irreducible tube domains of type $A$ can be realized as sub-variations of Hodge structure of certain variations which are naturally associated to families of abelian varieties of Weil type. The situations for tube domains of type $D^{\mathbb{H}}$ are also discussed. The second part of the thesis aims to understand the exceptional isomorphism between the Hermitian symmetric domains of type $\mathrm{II}_4$ and of type $\mathrm{IV}_6$ geometrically. We shall give some geometric constructions relating both of the domains to quaternionic covers of genus three curves. en_US dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US dc.format Monograph en_US dc.format.medium Electronic Resource en_US dc.language.iso en_US en_US dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US dc.subject.lcsh Mathematics en_US dc.subject.other Abelian variety, Calabi-Yau manifold, Hermitian symmetric domains, Variations of Hodge structure en_US dc.title On geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains en_US dc.type Dissertation en_US dc.mimetype Application/PDF en_US dc.contributor.committeemember Grushevsky, Samuel en_US dc.contributor.committeemember Schnell, Christian en_US dc.contributor.committeemember Chen, Qile. en_US
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