Calabi-Yau quotients with terminal singularities

TL;DR

This paper investigates quotients of Calabi-Yau threefolds with isolated singularities, focusing on cases where the quotient has terminal singularities, and establishes restrictions on the order of cyclic groups involved.

Contribution

It proves that for cyclic groups of prime order acting on Calabi-Yau threefolds resulting in terminal singularities, the group order must be 2, 3, or 5.

Findings

G must have order 2, 3, or 5 for terminal singularities

The analysis is restricted to cyclic groups of prime order

The work advances understanding of singularities in Calabi-Yau quotients

Abstract

In this paper we are interested in quotients of Calabi-Yau threefolds with isolated singularities. In particular, we analyze the case when $X/G$ has terminal singularities. We prove that, if $G$ is cyclic of prime order and $X/G$ has terminal singularities, then $G$ has order $2,3$ or $5$.