o-minimal GAGA and a conjecture of Griffiths

By Benjamin Bakker, Y. Brunebarbe, Jacob Tsimerman. Inventiones Mathematicae, 2018

80 citations recorded by the source corpus.

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 algebraic spaces are algebraic. Applying this to period maps, we conclude that the images of period maps are quasi-projective and that the restriction of the Griffiths bundle is ample.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ec1e4c0f3811ec30ce05e6a3c4a1dd814084a5aa

How researchers see this paper

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In Geometry and Topology

1. Bruno Klingler
2. E. Ullmo
3. G. Baldi
4. Jacob Tsimerman
5. Jonathan Pila
6. Ziyang Gao
7. A. Yafaev

In Mathematical Physics

1. Bruno Klingler
2. E. Ullmo
3. G. Baldi
4. Jacob Tsimerman
5. Jonathan Pila
6. Ziyang Gao
7. A. Yafaev

Citations in the corpus

• On the distribution of the Hodge locus (2021, background): “This is possible thanks to [4, Theorem 1.1], which asserts that the image of the period map is algebraic.”