Fano fourfolds with large anticanonical base locus
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866915242113499136 |
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| author | Höring, Andreas Secci, Saverio Andrea |
| author_facet | Höring, Andreas Secci, Saverio Andrea |
| contents | A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, hence has codimension two, all the anticanonical divisors are singular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_17029 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fano fourfolds with large anticanonical base locus Höring, Andreas Secci, Saverio Andrea Algebraic Geometry 14J45, 14J35, 14E30, 14J17 A famous theorem of Shokurov states that a general anticanonical divisor of a smooth Fano threefold is a smooth K3 surface. This is quite surprising since there are several examples where the base locus of the anticanonical system has codimension two. In this paper we show that for four-dimensional Fano manifolds the behaviour is completely opposite: if the base locus is a normal surface, hence has codimension two, all the anticanonical divisors are singular. |
| title | Fano fourfolds with large anticanonical base locus |
| topic | Algebraic Geometry 14J45, 14J35, 14E30, 14J17 |
| url | https://arxiv.org/abs/2309.17029 |