Foliations with isolated singularities on Hirzebruch surfaces

[EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the folia...

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Autores: Galindo Pastor, Carlos, Olivares, Jorge, Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
Tipo de recurso: artículo
Fecha de publicación:2021
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:10251/183574
Acceso en línea:https://riunet.upv.es/handle/10251/183574
Access Level:acceso abierto
Palabra clave:Foliations on surfaces
Singularities
MATEMATICA APLICADA
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spelling Foliations with isolated singularities on Hirzebruch surfacesGalindo Pastor, CarlosOlivares, JorgeMonserrat Delpalillo, Francisco José|||0000-0003-2221-0140Foliations on surfacesSingularitiesMATEMATICA APLICADA[EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For delta not equal 1, we prove that the singular scheme of F does not determine the foliation. However, we prove that, in most cases, two foliations F and F' given by sections s and s' have the same singular scheme if and only if s' = Phi(s), for some global endomorphism F of the tangent bundle of S-delta.The first two authors are partially supported by the Spanish Government MICINN/FEDER/AEI/UE, grants PGC2018-096446-B-C22 and RED2018-102583-T, as well as by Generalitat Valenciana, grant AICO2019-223 and Universitat Jaume I, grantUJI-2018-10. The third authorwas partially supported by CONACYT: Estancias Sabaticas Vinculadas a la Consolidacion de Grupos de Investigacion, CVU 10069.Walter de Gruyter GmbHDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería InformáticaUniversitat Jaume IGeneralitat ValencianaMinisterio de Educación y Ciencia e InnovaciónConsejo Nacional de Ciencia y Tecnología, MéxicoMinisterio de Ciencia, Innovación y UniversidadesRepositorio Institucional de la Universitat Politècnica de València Riunet20212021-10-10journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/183574reponame: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 2017-2020 PGC2018-096446-B-C22 VALORACIONES, FOLIACIONES Y CODIGOS CORRECTORES DE ERRORES CUANTICOSMinisterio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 RED2018-102583-TGeneralitat Valenciana https://doi.org/10.13039/501100003359 AICO%2F2019%2F223 Conjuntos convexos asociados a superficies y códigos correctores de erroresUniversitat Jaume I https://doi.org/10.13039/501100004834 UJI-2018-10Consejo Nacional de Ciencia y Tecnología, México https://doi.org/10.13039/501100003141 CVU 10069open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1835742026-06-13T07:49:27Z
dc.title.none.fl_str_mv Foliations with isolated singularities on Hirzebruch surfaces
title Foliations with isolated singularities on Hirzebruch surfaces
spellingShingle Foliations with isolated singularities on Hirzebruch surfaces
Galindo Pastor, Carlos
Foliations on surfaces
Singularities
MATEMATICA APLICADA
title_short Foliations with isolated singularities on Hirzebruch surfaces
title_full Foliations with isolated singularities on Hirzebruch surfaces
title_fullStr Foliations with isolated singularities on Hirzebruch surfaces
title_full_unstemmed Foliations with isolated singularities on Hirzebruch surfaces
title_sort Foliations with isolated singularities on Hirzebruch surfaces
dc.creator.none.fl_str_mv Galindo Pastor, Carlos
Olivares, Jorge
Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
author Galindo Pastor, Carlos
author_facet Galindo Pastor, Carlos
Olivares, Jorge
Monserrat Delpalillo, Francisco José|||0000-0003-2221-0140
author_role author
author2 Olivares, Jorge
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
Universitat Jaume I
Generalitat Valenciana
Ministerio de Educación y Ciencia e Innovación
Consejo Nacional de Ciencia y Tecnología, México
Ministerio de Ciencia, Innovación y Universidades
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Foliations on surfaces
Singularities
MATEMATICA APLICADA
topic Foliations on surfaces
Singularities
MATEMATICA APLICADA
description [EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For delta not equal 1, we prove that the singular scheme of F does not determine the foliation. However, we prove that, in most cases, two foliations F and F' given by sections s and s' have the same singular scheme if and only if s' = Phi(s), for some global endomorphism F of the tangent bundle of S-delta.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-10-10
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/10251/183574
url https://riunet.upv.es/handle/10251/183574
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 2017-2020 PGC2018-096446-B-C22 VALORACIONES, FOLIACIONES Y CODIGOS CORRECTORES DE ERRORES CUANTICOS
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 RED2018-102583-T
Generalitat Valenciana https://doi.org/10.13039/501100003359 AICO%2F2019%2F223 Conjuntos convexos asociados a superficies y códigos correctores de errores
Universitat Jaume I https://doi.org/10.13039/501100004834 UJI-2018-10
Consejo Nacional de Ciencia y Tecnología, México https://doi.org/10.13039/501100003141 CVU 10069
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Walter de Gruyter GmbH
publisher.none.fl_str_mv Walter de Gruyter GmbH
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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