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, Matsumoto-Sasaki-Yoshida
realized the moduli of six lines in $\mathbb{P}^2$ as arithmetic quotient
of Type IV domain of dimension 4 and studied its compactifications (both
GIT and Satake-Baily-Borel). On the other hand, Allcock-Carlson-Toledo
studied the moduli of smooth cubic threefolds as a 10-dimensional
arithmetic ball quotient. I will talk about a joint work with Zhiwei Zheng
about the moduli space of cubic fourfolds with automorphism group
specified, and moduli space of singular sextic curves. We realize them as
arithmetic quotients of balls or Type IV domains and compare their GIT and
Satake-Baily-Borel compactifications. This recovers many special examples
studied before.
Math-Physics Joint Seminar
Tuesday, September 18, 2018 - 4:30pm
Chenglong Yu
University of Pennsylvania