Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2018
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| Acceso en línea: | |
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| _version_ | 1866913340313305088 |
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| author | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús |
| author_facet | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús |
| contents | We consider rational surfaces $Z$ defined by divisorial valuations $ν$ of Hirzebruch surfaces. We introduce the concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice local and global equivalent conditions. In particular we prove that, when $ν$ is non-positive at infinity, the extremal rays of the cone of curves of $Z$ can be explicitly given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1811_10888 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Algebraic Geometry 14C20, 14E15, 13A18 We consider rational surfaces $Z$ defined by divisorial valuations $ν$ of Hirzebruch surfaces. We introduce the concepts of non-positivity and negativity at infinity for these valuations and prove that these concepts admit nice local and global equivalent conditions. In particular we prove that, when $ν$ is non-positive at infinity, the extremal rays of the cone of curves of $Z$ can be explicitly given. |
| title | Non-positive and negative at infinity divisorial valuations of Hirzebruch surfaces |
| topic | Algebraic Geometry 14C20, 14E15, 13A18 |
| url | https://arxiv.org/abs/1811.10888 |