On the explicit geometry of a certain blowing-up of a smooth quadric
Using the high symmetry in the geometry of a smooth projective quadric, we construct effectively new families of smooth projective rational surfaces whose nef divisors are regular, and whose effective monoids are finitely generated by smooth projective rational curves of negative self-intersection....
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Sciendo
2023-01-01
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| Series: | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/auom-2023-0004 |
| _version_ | 1811159190869114880 |
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| author | De La Rosa-Navarro B. L. Failla G. Frías-Medina J. B. Lahyane M. Utano R. |
| author_facet | De La Rosa-Navarro B. L. Failla G. Frías-Medina J. B. Lahyane M. Utano R. |
| author_sort | De La Rosa-Navarro B. L. |
| collection | DOAJ |
| description | Using the high symmetry in the geometry of a smooth projective quadric, we construct effectively new families of smooth projective rational surfaces whose nef divisors are regular, and whose effective monoids are finitely generated by smooth projective rational curves of negative self-intersection. Furthermore, the Cox rings of these surfaces are finitely generated, the dimensions of their anticanonical complete linear systems are zero, and their nonzero nef divisors intersect positively the anticanonical ones. And in two special cases, we give efficient ways of describing any effective divisor class in terms of the given minimal generating sets for the effective monoids of these surfaces. The ground field of our varieties is algebraically closed of arbitrary characteristic. |
| first_indexed | 2024-04-10T05:38:03Z |
| format | Article |
| id | doaj.art-a67ffbb97113422fad9f9773a12271a5 |
| institution | Directory Open Access Journal |
| issn | 1844-0835 |
| language | English |
| last_indexed | 2024-04-10T05:38:03Z |
| publishDate | 2023-01-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica |
| spelling | doaj.art-a67ffbb97113422fad9f9773a12271a52023-03-06T17:00:03ZengSciendoAnalele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica1844-08352023-01-01311719610.2478/auom-2023-0004On the explicit geometry of a certain blowing-up of a smooth quadricDe La Rosa-Navarro B. L.0Failla G.1Frías-Medina J. B.2Lahyane M.3Utano R.4Facultad de Ciencias, Universidad Autónoma de Baja California, Campus Ensenada, Ensenada, Baja California, MexicoUniversità Mediterranea di Reggio Calabria, Dipartimento DICEAM Via Graziella, Feo di Vito, Reggio Calabria, ItalyInstituto de Física y Matemáticas (IFM), Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3, Ciudad Universitaria, Morelia, Michoacán, MéxicoInstituto de Física y Matemáticas (IFM), Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3, Ciudad Universitaria, Morelia, Michoacán, MéxicoDipartimento di Scienze Matematiche e Informatiche Scienze Fisiche e Scienze della Terra, Università di Messina Viale Ferdinando Stagno D’Alcontres 31, 98166Messina, Italy.Using the high symmetry in the geometry of a smooth projective quadric, we construct effectively new families of smooth projective rational surfaces whose nef divisors are regular, and whose effective monoids are finitely generated by smooth projective rational curves of negative self-intersection. Furthermore, the Cox rings of these surfaces are finitely generated, the dimensions of their anticanonical complete linear systems are zero, and their nonzero nef divisors intersect positively the anticanonical ones. And in two special cases, we give efficient ways of describing any effective divisor class in terms of the given minimal generating sets for the effective monoids of these surfaces. The ground field of our varieties is algebraically closed of arbitrary characteristic.https://doi.org/10.2478/auom-2023-0004smooth projective quadric surfacenumerical equivalenceeffective monoidminimal modelinfinitely near pointscox ringsprimary 14c20, 14c22secondary 14j26 |
| spellingShingle | De La Rosa-Navarro B. L. Failla G. Frías-Medina J. B. Lahyane M. Utano R. On the explicit geometry of a certain blowing-up of a smooth quadric Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica smooth projective quadric surface numerical equivalence effective monoid minimal model infinitely near points cox rings primary 14c20, 14c22 secondary 14j26 |
| title | On the explicit geometry of a certain blowing-up of a smooth quadric |
| title_full | On the explicit geometry of a certain blowing-up of a smooth quadric |
| title_fullStr | On the explicit geometry of a certain blowing-up of a smooth quadric |
| title_full_unstemmed | On the explicit geometry of a certain blowing-up of a smooth quadric |
| title_short | On the explicit geometry of a certain blowing-up of a smooth quadric |
| title_sort | on the explicit geometry of a certain blowing up of a smooth quadric |
| topic | smooth projective quadric surface numerical equivalence effective monoid minimal model infinitely near points cox rings primary 14c20, 14c22 secondary 14j26 |
| url | https://doi.org/10.2478/auom-2023-0004 |
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