MMP for Enriques pairs and singular Enriques varieties
Francesco Antonio Denisi, \'Angel David R\'ios Ortiz, Nikolaos Tsakanikas, Zhixin Xie

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 and an effective -divisor on such that the pair is log canonical, we prove that any -MMP terminates with a minimal model of , where is a -factorial primitive Enriques variety with canonical singularities. Finally, we investigate the asymptotic theory of Enriques manifolds.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons
