Higher Albanese manifolds and maps are definable in o-minimal structures, and if a higher Albanese manifold of level at least three is algebraic, the tower stabilises at step two, making the pro-unipotent fundamental group at most 2-step nilpotent.
Quasi-projectivity of images of mixed period maps
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O-minimal geometry of higher Albanese manifolds
Higher Albanese manifolds and maps are definable in o-minimal structures, and if a higher Albanese manifold of level at least three is algebraic, the tower stabilises at step two, making the pro-unipotent fundamental group at most 2-step nilpotent.