Date of Award

Spring 5-15-2022

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



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


English (en)

Chair and Committee

Matt Kerr

Committee Members

Charles Doran

Included in

Mathematics Commons