Let us parametrize the set of lattices inside $\mathbb{C}^g$ with the open dense subset $U = \text{GL}_{2g}(\mathbb{R})$ of $\mathbb{R}^{4g^2}$. Does there exist a countable family $(Z_n)_{n \in \mathbb{N}}$ of algebraic real hypersurfaces of $\mathbb{R}^{4g^2}$ such that for every matrix $M \in U \setminus \bigcup_{n \in \mathbb{N}} Z_n$, the only complex subtori of $X = \mathbb{C}^g/\Gamma_M$ are $X$ and $\{0\}$?