Quasiprojectivity of images of mixed period maps

Quasiprojectivity of images of mixed period maps

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Benjamin Bakker, University of Illinois at Chicago

Zoom link:  https://princeton.zoom.us/j/91248028438

Families of smooth proper algebraic varieties give rise to variations of pure Hodge structures; general algebraic families yield variations of mixed Hodge structures. It was conjectured by Griffiths and proven in joint work with Y. Brunebarbe and J.Tsimerman that the closure of the image of the classifying map to the moduli space of Hodge structures is a quasiprojective algebraic variety in the pure case.  In this talk I will explain how to extend this result to the mixed setting. As in the pure case, the proof heavily uses techniques from o-minimal geometry, and we will also discuss some related applications.