Distribuation of CM points of an infinite series of complete Calabi-Yau moduli spaces

Abstract

In the infinite series of complete families of Calabi-Yau manifolds ${\tilde{f}}_n:{\tilde{\mathcal{X}}}_n\to {\mathfrak{M}}_{n,n+3}$, where $n$ is an odd number, arising from cyclic covers of ${\mathbb{P}}^n$ branching along hyperplane arrangements (\cite{SXZ13}), the set of CM points is dense for $n=1,3$ and finite for $n\ge 5$.

arXiv comment7 pages