\'{E}tale coverings in codimension 1 with applications to Mori Dream Spaces
Abstract
The present paper is devoted to developing relations between Galois \'etale coverings in codimension 1 and \'etale fundamental groups in codimension 1 of algebraic varieties, aimed to studying the topology of Mori dream spaces. In particular, the universal \'etale covering in codimension 1 of a non-degenerate toric variety and a canonical Galois \'etale covering in codimension 1 of a Mori dream space (MDS) are exhibited. Sufficient conditions for the latter being either still a MDS or the universal \'etale covering in codimension 1 are given. As an application, a canonical toric embedding of K3 universal coverings, of Enriques surfaces which are Mori dream, is described.
Keywords
Cite
@article{arxiv.1902.04784,
title = {\'{E}tale coverings in codimension 1 with applications to Mori Dream Spaces},
author = {Michele Rossi},
journal= {arXiv preprint arXiv:1902.04784},
year = {2025}
}
Comments
42 pages. v4: enumeration changed consistently with the published version