Date of Award
Doctor of Philosophy (PhD)
In this article, we review some aspects regarding Hodge-theoretic completion and boundarybehavior of period maps. First, we recall some classical results on compactification of classical period domains e.g. Baily-Borel, Ash-Mumford-Rapoport-Thai. The works produced by Kato-Usui aims at generalizing Mumford’s toroidal compactification to nonclassical period domain, which depends on construction of a strongly compatible fan. We prove such a fan can not exists universally, but for a single geometric variation of Hodge structure. We proceed such a construction on a 2-parameter geometric variation coming from Hosono-Takagi’s family of Calabi-Yau threefolds of type (1, 2, 2, 1). Moreover, we briefly review the concept of eigenspectra, which is directly generated from Steenbrink’s spectral theory on vanishing cohomology. We show by an example on how to compute the eigenspectra associated to a family
Chair and Committee
Deng, Haohua, "Hodge Theoretic Compactification of Period Maps" (2022). Arts & Sciences Electronic Theses and Dissertations. 2638.