School of Mathematics
https://hdl.handle.net/20.500.12111/14
School of Mathematics2023-01-26T14:19:11ZShafarevich mappings and period mappings
https://hdl.handle.net/20.500.12111/8041
Shafarevich mappings and period mappings
Griffiths, Phillip; Green, Mark; Katzarkov, Ludmil
We shall show that a smooth, quasi-projective variety X has a holomorphically convex universal covering eX when (i) 1(X) is residually nilpotent and (ii) there is an admissable variation of mixed Hodge structure over X whose monodromy representation has a nite kernel, and where in each case a corresponding period mapping is assumed to be proper.
I. Introduction and statements of results
II. The nilpotent case
III. The variation of Hodge structure and mixed Hodge structure cases
IV. Further directions
Hodge theory: What is it? How can it be used in algebraic geometry?
https://hdl.handle.net/20.500.12111/8031
Hodge theory: What is it? How can it be used in algebraic geometry?
Griffiths, Phillip
Lecture Slides
Extended Period Mappings
https://hdl.handle.net/20.500.12111/8030
Extended Period Mappings
Griffiths, Phillip
Clay Lecture at the INI, June 2022. The lecture is based on joint work with Mark Green and Colleen Robles. Theme of the lecture is global properties of period mappings with applications to the geometry of completions of moduli spaces.
Limits 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.