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

## TL;DR

This paper investigates the distribution of CM points in infinite series of Calabi-Yau moduli spaces, showing density for low dimensions and finiteness for higher dimensions.

## Contribution

It provides a detailed analysis of CM point distribution across an infinite series of Calabi-Yau moduli spaces arising from cyclic covers, highlighting dimension-dependent behavior.

## Key findings

- CM points are dense for n=1, 3
- CM points are finite for n≥5
- Distribution behavior varies with dimension

## Abstract

In the infinite series of complete families of Calabi-Yau manifolds $\tilde{f}_n: \tilde{\mathcal{X}}_n\rightarrow \mathfrak{M}_{n, n+3}$, 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 $n\geq 5$.