We prove the existence of global sections trivializing the Hodge bundles on the Hodge metric completion space of the Torelli space of Calabi-Yau manifolds, a global splitting property of these Hodge bundles. We also prove that a compact Calabi-Yau manifold can not be deformed to its complex conjugate. These results answer certain open questions in the subject. A general result about certain period map to be bi-holomorphic from the Hodge metric completion space of the Torelli space of Calabi-Yau type manifolds to their period domains is proved and applied to the cases of K3 surfaces, cubic fourfolds, and hyperKähler manifolds.
CITATION STYLE
Liu, K., Shen, Y., & Chen, X. (2016). Applications of the affine structures on the teichmüller spaces. In Springer Proceedings in Mathematics and Statistics (Vol. 154, pp. 59–79). Springer New York LLC. https://doi.org/10.1007/978-4-431-56021-0_3
Mendeley helps you to discover research relevant for your work.