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...

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Autores: Galindo, Carlos, Moreno-Ávila, Carlos Jesús, Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
Formato: artículo
Fecha de publicación:2025
País:España
Recursos: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
Acesso em linha:https://riunet.upv.es/handle/10251/226598
Access Level:acceso abierto
Palavra-chave:Finite generation of the cone of curves
Arrowed proximity graph
Mori dream spaces
Bounded negativity conjecture
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spelling The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfacesGalindo, CarlosMoreno-Ávila, Carlos JesúsMonserrat Delpalillo, Francisco José|||0000-0003-2221-0140Finite generation of the cone of curvesArrowed proximity graphMori dream spacesBounded negativity conjecture[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.The authors were partially funded by MCIN/AEI/10.13039/501100011033 and by ERDF, UE, grant PID2022-138906NB-C22, as well as by Universitat Jaume I, grant GACUJIMA- 2024-03. The third author was also supported by the Margarita Salas postdoctoral contract MGS/2021/14(UP2021-021) financed by the European Union- NextGenerationEU. Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaEuropean CommissionUniversitat Jaume IAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20252025-07-12journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/226598reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-138906NB-C22 SISTEMAS LINEALES Y POSITIVIDAD. FOLIACIONES. CODIGOS CUANTICOS Y LOCALMENTE RECUPERABLESEuropean Commission https://doi.org/10.13039/501100000780 NextGenerationEU MGS%2F2021%2F14Universitat Jaume I https://doi.org/10.13039/501100004834 GACUJIMA-2024-03open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/2265982026-06-13T07:49:27Z
dc.title.none.fl_str_mv The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
title The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
spellingShingle The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
Galindo, Carlos
Finite generation of the cone of curves
Arrowed proximity graph
Mori dream spaces
Bounded negativity conjecture
title_short The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
title_full The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
title_fullStr The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
title_full_unstemmed The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
title_sort The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces
dc.creator.none.fl_str_mv Galindo, Carlos
Moreno-Ávila, Carlos Jesús
Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
author Galindo, Carlos
author_facet Galindo, Carlos
Moreno-Ávila, Carlos Jesús
Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
author_role author
author2 Moreno-Ávila, Carlos Jesús
Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Informática
European Commission
Universitat Jaume I
Agencia Estatal de Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Finite generation of the cone of curves
Arrowed proximity graph
Mori dream spaces
Bounded negativity conjecture
topic Finite generation of the cone of curves
Arrowed proximity graph
Mori dream spaces
Bounded negativity conjecture
description [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.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025-07-12
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/226598
url https://riunet.upv.es/handle/10251/226598
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023 PID2022-138906NB-C22 SISTEMAS LINEALES Y POSITIVIDAD. FOLIACIONES. CODIGOS CUANTICOS Y LOCALMENTE RECUPERABLES
European Commission https://doi.org/10.13039/501100000780 NextGenerationEU MGS%2F2021%2F14
Universitat Jaume I https://doi.org/10.13039/501100004834 GACUJIMA-2024-03
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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