School of MathematicsSchool of Mathematicshttps://hdl.handle.net/20.500.12111/142021-04-10T05:22:05Z2021-04-10T05:22:05ZTopics in the geometric application of Hodge theoryGriffiths, Philliphttps://hdl.handle.net/20.500.12111/79432021-04-01T18:00:17ZTopics in the geometric application of Hodge theory
Griffiths, Phillip
The classifcation of algebraic varieties is a central part of algebraic geometry. Among the common tools that are employed are birational geometry, especially using the analysis of singularities, and Hodge theory. The latter is frequently used as a sort of "black box": the cohomology of an algebraic variety has a functorial mixed Hodge structure and the formal properties of the corresponding category have very strong consequences.
On the other hand, geometric structures arise naturally in Hodge theory and one aspect of this will be the focus of these lectures. This aspect originates from the fact that mixed Hodge structures have extension data expressed by linear algebra.
Lectures given at the University of Miami, spring 2021.
Towards a maximal completion of a period mapGriffiths, PhillipGreen, MarkRobles, Colleenhttps://hdl.handle.net/20.500.12111/79372021-02-19T21:00:18Z2021-02-11T00:00:00ZTowards 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 mappingsGriffiths, PhillipGreen, MarkRobles, Colleenhttps://hdl.handle.net/20.500.12111/79362021-02-19T21:00:17Z2021-02-11T00:00:00ZNatural 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 MappingsGriffiths, PhillipGreen, MarkRobles, Colleenhttps://hdl.handle.net/20.500.12111/79252020-10-16T14:00:12Z2020-10-13T00:00:00ZCompletions 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
2020-10-13T00:00:00Z