School of Mathematics
https://hdl.handle.net/20.500.12111/14
School of Mathematics2022-05-16T06:12:41ZLimits in Hodge Theory
https://hdl.handle.net/20.500.12111/7980
Limits in Hodge Theory
Griffiths, Phillip
Almost all of the deep results in Hodge theory and its applications to algebraic geometry require understanding the limits in a family of Hodge structures. In the literature the proofs of these results frequently use the consequences of the analysis of the singularities acquired in a degenerating family of Hodge structures; that analysis itself is treated as a "black box." In these lectures an attempt will be made to give an informal introduction to the subject of limits of Hodge structures and to explain some of the essential ideas of the proofs. One additional topic not yet in the literature that we will discuss is the geometric interpretation of the extension data in limiting mixed Hodge structures and its use in moduli questions.
Lecture series at the University of Miami in Spring 2022.
Extended Period Mappings
https://hdl.handle.net/20.500.12111/7979
Extended Period Mappings
Griffiths, Phillip
This lecture will discuss the global structure of period mappings (variation of Hodge structure) defined over complete, 2-dimensional algebraic varieties. Some applications to moduli of general type algebraic surfaces will also be presented.
Clay Lecture at INI in June 2022. Based on joint work with Mark Green and Colleen Robles.
Differential of a period mapping at a singularity
https://hdl.handle.net/20.500.12111/7977
Differential of a period mapping at a singularity
Griffiths, Phillip; Green, Mark
To Herb Clemens. Lefschetz wrote that he put the harpoon of topology into the whale of algebraic geometry. Herb but the harpoon of topology into the whale of Hodge theory.
Period mappings, or equivalently variations of Hodge structure, have been used both to study families of algebraic varieties and as a subject in its own right.
2021-01-01T00:00:00ZCompletions of Period Mappings: Progress Report
https://hdl.handle.net/20.500.12111/7951
Completions of Period Mappings: Progress Report
Griffiths, Phillip; Green, Mark; Robles, Colleen
We give an informal, expository account of a project to construct completions
of period maps.
2021-01-01T00:00:00Z