MMP for Enriques pairs and singular Enriques varieties

• Main Authors: Denisi, Francesco Antonio, Ortiz, Ángel David Ríos, Tsakanikas, Nikolaos, Xie, Zhixin
• Format: Journal Article
• Language: English
• Published: 18-09-2024
• Subjects: Mathematics - Algebraic Geometry
• DOI: 10.48550/arxiv.2409.12054

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.