MMP for Enriques pairs and singular Enriques varieties

TL;DR

This paper introduces primitive Enriques varieties, studies their stability under the Minimal Model Program, and explores their asymptotic properties, expanding understanding of Enriques manifolds and their singular counterparts.

Contribution

It defines primitive Enriques varieties, proves their stability under MMP, and analyzes the asymptotic behavior of Enriques manifolds.

Findings

Primitive Enriques varieties are stable under MMP.

Any log canonical pair on an Enriques manifold terminates with a primitive Enriques variety.

The paper advances the understanding of singular Enriques varieties and their minimal models.

Abstract

We introduce and study the class of primitive Enriques varieties, whose smooth members are Enriques manifolds. We provide several examples and we demonstrate that this class is stable under the operations of the Minimal Model Program (MMP). In particular, given an Enriques manifold $Y$ and an effective $\mathbb{R}$-divisor $B_Y$ on $Y$ such that the pair $(Y,B_Y)$ is log canonical, we prove that any $(K_Y+B_Y)$-MMP terminates with a minimal model $(Y',B_{Y'})$ of $(Y,B_Y)$, where $Y'$ is a $\mathbb{Q}$-factorial primitive Enriques variety with canonical singularities. Finally, we investigate the asymptotic theory of Enriques manifolds.