Étale coverings in codimension 1 with applications to Mori Dream Spaces
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866909677720174592 |
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| author | Rossi, Michele |
| author_facet | Rossi, Michele |
| contents | The present paper is devoted to developing relations between Galois étale coverings in codimension 1 and étale fundamental groups in codimension 1 of algebraic varieties, aimed to studying the topology of Mori dream spaces. In particular, the universal étale covering in codimension 1 of a non-degenerate toric variety and a canonical Galois étale 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 étale 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1902_04784 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Étale coverings in codimension 1 with applications to Mori Dream Spaces Rossi, Michele Algebraic Geometry 14H30, 14E20, 14M25, 14E30 The present paper is devoted to developing relations between Galois étale coverings in codimension 1 and étale fundamental groups in codimension 1 of algebraic varieties, aimed to studying the topology of Mori dream spaces. In particular, the universal étale covering in codimension 1 of a non-degenerate toric variety and a canonical Galois étale 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 étale 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. |
| title | Étale coverings in codimension 1 with applications to Mori Dream Spaces |
| topic | Algebraic Geometry 14H30, 14E20, 14M25, 14E30 |
| url | https://arxiv.org/abs/1902.04784 |