For special Gushel-Mukai threefolds, the invariant part of the infinitesimal period map is injective, and the kernel of the full period map has dimension exactly three.
The desingularization of the theta divisor of a cubic threefold as a moduli space
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Infinitesimal Torelli problems for special Gushel-Mukai and related Fano threefolds: Hodge theoretical and categorical perspectives
For special Gushel-Mukai threefolds, the invariant part of the infinitesimal period map is injective, and the kernel of the full period map has dimension exactly three.