Type
Text
Type
Dissertation
Advisor
Grushevsky, Samuel | Laza, Radu | Schnell, Christian | Chen, Qile.
Date
2014-12-01
Keywords
Mathematics | Abelian variety, Calabi-Yau manifold, Hermitian symmetric domains, Variations of Hodge structure
Department
Department of Mathematics.
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76418
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
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. | 91 pages
Recommended Citation
Zhang, Zheng, "On geometric and motivic realizations of variations of Hodge structure over Hermitian symmetric domains" (2014). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2341.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2341