Logarithmic Enriques varieties

TL;DR

This paper introduces logarithmic Enriques varieties as a new class of singular analogues to Enriques manifolds, extending the concept of log-Enriques surfaces, and explores their properties and examples, especially those with symplectic covers.

Contribution

It defines logarithmic Enriques varieties, generalizes existing notions, and studies their properties and examples, particularly those with quasi-étale symplectic covers.

Findings

Many examples of logarithmic Enriques varieties are provided.

Properties of those admitting quasi-étale symplectic covers are analyzed.

The notion extends the concept of log-Enriques surfaces to higher dimensions.

Abstract

We introduce logarithmic Enriques varieties as a singular analogue of Enriques manifolds, generalizing the notion of log-Enriques surfaces introduced by Zhang. We focus then on the properties of the subfamily of log-Enriques varieties that admit a quasi-\'etale cover by a singular symplectic variety and we give many examples.