Rational surfaces with finitely generated Cox rings and very high Picard numbers
| Autor: | Brenda Leticia De La Rosa-Navarro, Mustapha Lahyane, Juan Bosco Frías-Medina |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Algebra and Number Theory Applied Mathematics 010102 general mathematics Base field 01 natural sciences Blowing up Computational Mathematics 0103 physical sciences 010307 mathematical physics Geometry and Topology Finitely-generated abelian group 0101 mathematics Algebraically closed field Analysis Mathematics |
| Zdroj: | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 111:297-306 |
| ISSN: | 1579-1505 1578-7303 |
| Popis: | In this paper, we provide new families of smooth projective rational surfaces whose Cox rings are finitely generated. These surfaces are constructed by blowing-up points in Hirzebruch surfaces and may have very high Picard numbers. Such construction is not straightforward, and we achieve our results using the facts that these surfaces are extremal, and their effective monoids are finitely generated. Furthermore, we give an example illustrating the existence of rational surfaces which are not extremal. The base field of our varieties is assumed to be algebraically closed of arbitrary characteristic. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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