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arXiv · 1902.04784

\'{E}tale coverings in codimension 1 with applications to Mori Dream Spaces

Michele Rossi
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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.

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Michele Rossi. 2019-02-13. \'{E}tale coverings in codimension 1 with applications to Mori Dream Spaces. https://doi.org/10.1007/s40879-025-00838-5

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