The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
[EN] Let X be a rational surface obtained by blowing up a configuration C of infinitely near points over a Hirzebruch surface F_delta. We prove that there exist two positive integers a ≤ b such that the cone of curves of X is finite polyhedral and minimally generated whenever delta ≥ a, and the Cox...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2025 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/226598 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/226598 |
| Access Level: | acceso abierto |
| Palabra clave: | Finite generation of the cone of curves Arrowed proximity graph Mori dream spaces Bounded negativity conjecture |
| Sumario: | [EN] Let X be a rational surface obtained by blowing up a configuration C of infinitely near points over a Hirzebruch surface F_delta. We prove that there exist two positive integers a ≤ b such that the cone of curves of X is finite polyhedral and minimally generated whenever delta ≥ a, and the Cox ring of X is finitely generated whenever delta ≥ b. The integers a and b depend only on a combinatorial object (a graph decorated with arrows) that represents the strict transforms of the exceptional divisors, their intersections, and their intersections with the fibers and the special section of F_delta. |
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