Maximal Families of Calabi–Yau Manifolds with Minimal Length Yukawa Coupling

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 -PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.