Quebec Mathematical Sciences Colloquium

October 9, 2020 from 15:00 to 16:00 (Montreal/Miami time) Zoom meeting

Hodge Theory and Moduli

Colloquium presented by Phillip Griffiths (Institute for Advanced Study, Princeton, USA)

The theory of moduli is an important and active area in algebraic geometry. For varieties of general type the existence of a moduli space with a canonical completion has been proved by Kollar/Shepard-Barron/Alexeev. Aside from the classical case of algebraic curves, very little is known about the structure of , especially it’s boundary. The period mapping from Hodge theory provides a tool for studying these issues.

In this talk, we will discuss some aspects of this topic with emphasis on I-surfaces, which provide one of the first examples where the theory has been worked out in some detail. Particular notice will me made of how the extension data in the limiting mixed Hodge structures that arise from singular surfaces on the boundary of moduli may be used to guide the desingularization of that boundary. 

Hodge Theory and Moduli