Geometry Seminar

Date: April 9, 2018

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Zhiwei Zheng, Tsinghua University

Title: Moduli of Symmetric Cubic Fourfolds

Abstract: The period map is a powerful tool to study moduli spaces of many kinds of objects related to K3 surfaces and cubic fourfolds, thanks to the global Torelli theorems. In this spirit, Allcock-Carlson-Toledo (2003) realized the moduli of smooth cubic threefolds as an arrangement complement in a 10-dimensional arithmetic ball quotient and studied its compactifications (both GIT and Satake-Baily-Borel) and recently, Laza-Pearlstein-Zhang studied the moduli of pairs consisting of a cubic threefold and a hyperplane section. I will talk about a joint work with Chenglong Yu about the moduli space of cubic fourfolds with automorphism group specified, and its compactification. As examples, we recover some of the works by Allcock-Carlson-Toledo and Laza-Pearlstein-Zhang mentioned above.