The cone of curves and the Cox ring of rational surfaces given by divisorial valuations
We consider surfaces X defined by plane divisorial valuations v of the quotient field of the local ring R at a closed point p of the projective plane P-2 over an arbitrary algebraically closed field k and centered at R. We prove that the regularity of the cone of curves of X is equivalent to the fac...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| 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:10251/84800 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/84800 |
| Access Level: | acceso abierto |
| Palabra clave: | Cone of curves Cox ring Rational surfaces Plane divisorial valuation |
| Sumario: | We consider surfaces X defined by plane divisorial valuations v of the quotient field of the local ring R at a closed point p of the projective plane P-2 over an arbitrary algebraically closed field k and centered at R. We prove that the regularity of the cone of curves of X is equivalent to the fact that v is non-positive on Op(2) (P-2 \ L), where L is a certain line containing p. Under these conditions, we characterize when the characteristic cone of X is closed and its Cox ring finitely generated. Equivalent conditions to the fact that v is negative on Opt (P-2 \ L) k are also given. (C) 2015 Published by Elsevier Inc. |
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