<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

On the explicit geometry of a certain blowing-up of a smooth quadric

Università Mediterranea di Reggio Calabria

Dipartimento DICEAM Via Graziella, Feo di Vito, Reggio Calabria

Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3

Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3, Ciudad Universitaria

Dipartimento di Scienze Matematiche e Informatiche Scienze Fisiche e Scienze della Terra

Università di Messina Viale Ferdinando Stagno D’Alcontres 31

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"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...

On the explicit geometry of a certain blowing-up of a smooth quadric

Online veröffentlicht: 04. Feb. 2023

Seitenbereich: 71 - 96

Eingereicht: 08. März 2022

Akzeptiert: 15. Juni 2022

DOI: https://doi.org/10.2478/auom-2023-0004

Schlüsselwörter
Smooth Projective Quadric Surface, Numerical Equivalence, Effective Monoid, Minimal Model, Infinitely Near Points, Cox Rings

© 2023 B. L. De La Rosa-Navarro et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

On the explicit geometry of a certain blowing-up of a smooth quadric

Online veröffentlicht: 04. Feb. 2023

Seitenbereich: 71 - 96

Eingereicht: 08. März 2022

Akzeptiert: 15. Juni 2022

DOI: https://doi.org/10.2478/auom-2023-0004

SchlüsselwörterSmooth Projective Quadric Surface, Numerical Equivalence, Effective Monoid, Minimal Model, Infinitely Near Points, Cox Rings

© 2023 B. L. De La Rosa-Navarro et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Smooth Projective Quadric Surface, Numerical Equivalence, Effective Monoid, Minimal Model, Infinitely Near Points, Cox Rings