School of Mathematics
https://hdl.handle.net/20.500.12111/14
School of Mathematics2021-03-09T05:51:20ZTowards a maximal completion of a period map
https://hdl.handle.net/20.500.12111/7937
Towards a maximal completion of a period map
Griffiths, Phillip; Green, Mark; Robles, Colleen
The motivation behind this work is to construct a "Hodge theoretically maximal" completion of a period map. This is done up to finite data (we work with the Stein factorization of the period map). The image of the extension is a Moishezon variety that compactifies a finite cover of the image of the period map.
2021-02-11T00:00:00ZNatural line bundles on completions of period mappings
https://hdl.handle.net/20.500.12111/7936
Natural line bundles on completions of period mappings
Griffiths, Phillip; Green, Mark; Robles, Colleen
We give conditions under which natural lines bundles associated with completions of period mappings are semi-ample and ample.
2021-02-11T00:00:00ZCompletions 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.