# o-minimal GAGA and a conjecture of Griffiths

@article{Bakker2018ominimalGA, title={o-minimal GAGA and a conjecture of Griffiths}, author={Benjamin Bakker and Yohan Brunebarbe and Jacob Tsimerman}, journal={arXiv: Algebraic Geometry}, year={2018} }

We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are definable with respect to a given o-minimal structure, and prove a GAGA-type theorem algebraizing definable coherent sheaves on complex algebraic spaces. We then combine this with algebraization theorems of Artin to show that proper definable images of complex…

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