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.
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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.