| dc.identifier.uri | http://hdl.handle.net/11401/76418 | |
| 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 | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.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. | |
| dcterms.available | 2017-09-20T16:50:11Z | |
| dcterms.contributor | Grushevsky, Samuel | en_US |
| dcterms.contributor | Laza, Radu | en_US |
| dcterms.contributor | Schnell, Christian | en_US |
| dcterms.contributor | Chen, Qile. | en_US |
| dcterms.creator | Zhang, Zheng | |
| dcterms.dateAccepted | 2017-09-20T16:50:11Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:11Z | |
| dcterms.description | Department of Mathematics. | en_US |
| dcterms.extent | 91 pg. | en_US |
| dcterms.format | Monograph | |
| dcterms.format | Application/PDF | en_US |
| dcterms.identifier | http://hdl.handle.net/11401/76418 | |
| dcterms.issued | 2014-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:11Z (GMT). No. of bitstreams: 1
Zhang_grad.sunysb_0771E_12170.pdf: 635223 bytes, checksum: e86df90ddbd449578db696660f0d8aa9 (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Abelian variety, Calabi-Yau manifold, Hermitian symmetric domains, Variations of Hodge structure | |
| dcterms.subject | Mathematics | |
| dcterms.title | On geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains | |
| dcterms.type | Dissertation | |
