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

Abstract

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 ${\mathbb{Q}}$-PVHS of the family uniformizing a Zariski open subset of an arithmetic ball quotient.

Keywords

Calabi–Yau / Yukawa Coupling / Hodge Theory

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