Nef divisors of surfaces given by pencils at infinity
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918343274921984 |
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| author | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira |
| author_facet | Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira |
| contents | We give generators for the nef cone and the cone of curves of rational surfaces obtained by blowing-up the complex projective plane at a set of points $\mathcal{B} \cup \mathcal{D}$, where $\mathcal{B}$ is the set of (proper and infinitely near) base points of a pencil associated with a curve having one place at infinity, and $\mathcal{D}$ is a set of finitely many infinitely near free points on the strict transforms of curves of the pencil. We also prove that, when the pencil is given by an AMS-type curve and $\mathcal{D}$ contains at most two free points on any curve considered, the Cox ring of the obtained surface is finitely generated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nef divisors of surfaces given by pencils at infinity Galindo, Carlos Monserrat, Francisco Moreno-Ávila, Carlos-Jesús Pérez-Callejo, Elvira Algebraic Geometry 14C20, 14E15, 14C21 We give generators for the nef cone and the cone of curves of rational surfaces obtained by blowing-up the complex projective plane at a set of points $\mathcal{B} \cup \mathcal{D}$, where $\mathcal{B}$ is the set of (proper and infinitely near) base points of a pencil associated with a curve having one place at infinity, and $\mathcal{D}$ is a set of finitely many infinitely near free points on the strict transforms of curves of the pencil. We also prove that, when the pencil is given by an AMS-type curve and $\mathcal{D}$ contains at most two free points on any curve considered, the Cox ring of the obtained surface is finitely generated. |
| title | Nef divisors of surfaces given by pencils at infinity |
| topic | Algebraic Geometry 14C20, 14E15, 14C21 |
| url | https://arxiv.org/abs/2602.15703 |