Finite-order translation conjecture for characteristic varieties

Let $X$ be the divisor germ under consideration and let the characteristic variety be viewed inside

$$\operatorname{Spec}\mathbf{C}[\pi_1(\partial B_{\epsilon}-\partial B_{\epsilon}\cap X)].$$

A translated subtorus is a subtorus translated by a character, and a translation is of finite order when that character is a torsion point.

Finite-order translation conjecture. The characteristic variety is a union of translated subtori, with each translation given by a point of finite order.

The preceding theorem identifies components arising from exponents of polytopes of quasiadjunction and shows that these components are translated subgroups by points of finite order. The conjecture asserts that all characteristic-variety components have this form.