If a degenerating threefold has canonical singularities, the moduli space of pairs of P^3 and hypersurfaces is smooth at the corresponding point.
Koll´ ar,Families of varieties of general type, Cambridge Tracts in Mathematics, 231, Cambridge University Press, Cambridge
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Deformation of pairs of $\mathbb{P}^3$ and hypersurfaces
If a degenerating threefold has canonical singularities, the moduli space of pairs of P^3 and hypersurfaces is smooth at the corresponding point.