Quasi-projectivity of images of mixed period maps
-
Benjamin Bakker
,
Yohan Brunebarbe
Abstract
We prove a mixed version of a conjecture of Griffiths: that the closure of the image of any admissible mixed period map is quasi-projective, with a natural ample bundle. Specifically, we consider the map from the image of the mixed period map to the image of the period map of the associated graded. On the one hand, we show in a precise manner that the parts of this map parametrizing extension data of non-adjacent-weight pure Hodge structures are quasi-affine. On the other hand, extensions of adjacent-weight pure polarized Hodge structures are parametrized by a compact complex torus (the intermediate Jacobian) equipped with a natural theta bundle which is ample in Griffiths transverse directions.
Our proof makes heavy use of o-minimality, and recent work with B. Klingler associating an
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1702149
Award Identifier / Grant number: DMS-1848049
Funding statement: Benjamin Bakker was partially supported by NSF grants DMS-1702149 and DMS-1848049.
Acknowledgements
Yohan Brunebarbe would like to thank P. Brosnan for an interesting discussion related to the biextension bundle.
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Proof of the Michael–Simon–Sobolev inequality using optimal transport
- Existence and symmetry of periodic nonlocal-CMC surfaces via variational methods
- Semi-continuity of conductors, and ramification bound of nearby cycles
- The integrality conjecture and the cohomology of preprojective stacks
- Graphical solutions to one-phase free boundary problems
- Quasi-projectivity of images of mixed period maps
- Higher order Kirillov--Reshetikhin modules for 𝐔 q (A n (1)), imaginary modules and monoidal categorification
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Articles in the same Issue
- Frontmatter
- Proof of the Michael–Simon–Sobolev inequality using optimal transport
- Existence and symmetry of periodic nonlocal-CMC surfaces via variational methods
- Semi-continuity of conductors, and ramification bound of nearby cycles
- The integrality conjecture and the cohomology of preprojective stacks
- Graphical solutions to one-phase free boundary problems
- Quasi-projectivity of images of mixed period maps
- Higher order Kirillov--Reshetikhin modules for 𝐔 q (A n (1)), imaginary modules and monoidal categorification
- The set of local 𝐴-packets containing a given representation
