Unobstructedness conjecture for non-rigid Calabi–Yau families

Let $\mathscr M_h$ be a moduli space of polarized Calabi–Yau manifolds with fixed Hilbert polynomial $h$, and let

$$\gamma:(H_1,S_1)\times(H_2,S_2)\to(\overline{\mathscr M}_h,D_\infty)$$

be a maximal extension of a non-rigid log map, with restricted source curves $(C,S_C)\times\{b\}$ and $\{a\}\times(T,S_T)$.

Unobstructedness conjecture. The deformations of both restricted log maps are unobstructed for all $a\in H_1$ and $b\in H_2$.

This conjecture is introduced as crucial for establishing the specialness of bi-Hom schemes. Its resolution is not specified in the source.