Penn Arts & Sciences Logo

Math-Physics Joint Seminar

Tuesday, September 18, 2018 - 4:30pm

Chenglong Yu

University of Pennsylvania


University of Pennsylvania

DRL 4c2

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.

Stream Video URL

Download Video URL