School of Mathematics
https://hdl.handle.net/20.500.12111/14
School of Mathematics2020-11-22T08:42:29ZCompletions of Period Mappings
https://hdl.handle.net/20.500.12111/7925
Completions of Period Mappings
Griffiths, Phillip; Green, Mark; Robles, Colleen
This work initiates a global study of period mappings at infinity, that is motivated by challenges arising when considering the questions:
(i) What are natural completions of a period mapping?
(ii) What geometric applications do they have?
arXiv:2010.06720
2020-10-13T00:00:00ZHodge theory and Moduli
https://hdl.handle.net/20.500.12111/7924
Hodge theory and Moduli
Griffiths, Phillip
The theory of moduli is an important and active area in algebraic geometry. For varieties of general type the existence of a moduli space $\mathcal{M}$ with a canonical completion $\bar{\mathcal{M}}$ has been proved by Koll\'ar/Shepard-Barron/Alexeev. Aside from the classical case of algebraic curves, very little is known about the structure of $\mathcal{M}$, especially it's boundary $\overline{\mathcal{M}} \diagdown\mathcal{M}$. 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.
CRM/ISM Colloquium lecture given in Montreal, October 9, 2020.
Some geometric applications of Hodge theory (Talks in Chile and Montreal)
https://hdl.handle.net/20.500.12111/7923
Some geometric applications of Hodge theory (Talks in Chile and Montreal)
Griffiths, Phillip
Hodge theory is a subject of both interest in it's own right and as a tool for studying geometric questions. This talk will be mainly concerned with some of the history and uses of Hodge theory: how did it originate and what are some of the ways it helps to address problems in geometry, especially algebraic geometry? Our discussion of both the early history and uses of Hodge theory will be selective, not comprehensive.
Lecture slides for talk give at virtual conference for Research Center Geometry at the Frontier in October of 2020 and the Montreal Geometry and Topology seminar (CIRGET) in November 2020.
Completions of Period Mappings
https://hdl.handle.net/20.500.12111/7922
Completions of Period Mappings
Griffiths, Phillip
*Notes of a talk given at IMSA at the University of Miami, October 5, 2020. Based on work in progress with Mark Green and Colleen Robles. An earlier version of these notes is in
https://hdl.handle.net/20.500.12111/7910.