For each natural odd number n ≥ 3, we exhibit a maximal family of
n-dimensional Calabi–Yau manifolds whose Yukawa coupling length is 1. As a consequence, Shafarevich’s conjecture holds true for these families. Moreover, it follows from Deligne and Mostow (Publ. Math. IHÉS, 63:5–89, 1986) and Mostow
(Publ. Math. IHÉS, 63:91–106, 1986; J. Am. Math. Soc., 1(3):555–586, 1988) that,
for n = 3, it can be partially compactified to a Shimura family of ball type, and for
n = 5,9, there is a sub Q-PVHS of the family uniformizing a Zariski open subset of
an arithmetic ball quotient