Integrable Systems and projective images of Kummer surfaces

Autores
Piovan, Luis Amadeo; Vanhaecke, Pol
Año de publicación
2000
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The (-1 )-involution on the Jacobian Jr of an arbitrary Riemann surfacer of genus two leads to a singular surface, the Kummer surface Icr of Jr, which,after desingularization, defines a X-3 surface Kr . We consider ample line bundleson Kr coming from the even or odd sections of [n O] with prescribed vanishingat the 2-division points of Jr (0 is the theta divisor of Jr). We use an integrablesystem to show that in the cases we study the linear system is base-point-free,to determine which curves are contracted to singular points and to compute anexplicit equation for the surface in projective space. Our explicit methods applyto the Kummer surface of any Abelian surface, given as the fiber of the momentmap of an algebraic completely integrable system.
Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Vanhaecke, Pol. Université de Poitiers; Francia
Materia
Integrable Systems
Abelian Surfaces
Kummer Surfaces
K 3 Surfaces
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/80939
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/80939
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Integrable Systems and projective images of Kummer surfacesPiovan, Luis AmadeoVanhaecke, PolIntegrable SystemsAbelian SurfacesKummer SurfacesK 3 Surfaceshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1The (-1 )-involution on the Jacobian Jr of an arbitrary Riemann surfacer of genus two leads to a singular surface, the Kummer surface Icr of Jr, which,after desingularization, defines a X-3 surface Kr . We consider ample line bundleson Kr coming from the even or odd sections of [n O] with prescribed vanishingat the 2-division points of Jr (0 is the theta divisor of Jr). We use an integrablesystem to show that in the cases we study the linear system is base-point-free,to determine which curves are contracted to singular points and to compute anexplicit equation for the surface in projective space. Our explicit methods applyto the Kummer surface of any Abelian surface, given as the fiber of the momentmap of an algebraic completely integrable system.Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Vanhaecke, Pol. Université de Poitiers; FranciaScuola Normale Superiore2000-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/80939Piovan, Luis Amadeo; Vanhaecke, Pol; Integrable Systems and projective images of Kummer surfaces; Scuola Normale Superiore; Annali Della Scuola Normale Superiore Di Pisa Cl. Di Scienze - Iv; XXIX; 2; 10-2000; 351-3920391-173XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.numdam.org/article/ASNSP_2000_4_29_2_351_0.pdfinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:40:39Zoai:ri.conicet.gov.ar:11336/80939instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-10-15 14:40:39.367CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Integrable Systems and projective images of Kummer surfaces
title Integrable Systems and projective images of Kummer surfaces
spellingShingle Integrable Systems and projective images of Kummer surfaces
Piovan, Luis Amadeo
Integrable Systems
Abelian Surfaces
Kummer Surfaces
K 3 Surfaces
title_short Integrable Systems and projective images of Kummer surfaces
title_full Integrable Systems and projective images of Kummer surfaces
title_fullStr Integrable Systems and projective images of Kummer surfaces
title_full_unstemmed Integrable Systems and projective images of Kummer surfaces
title_sort Integrable Systems and projective images of Kummer surfaces
dc.creator.none.fl_str_mv Piovan, Luis Amadeo
Vanhaecke, Pol
author Piovan, Luis Amadeo
author_facet Piovan, Luis Amadeo
Vanhaecke, Pol
author_role author
author2 Vanhaecke, Pol
author2_role author
dc.subject.none.fl_str_mv Integrable Systems
Abelian Surfaces
Kummer Surfaces
K 3 Surfaces
topic Integrable Systems
Abelian Surfaces
Kummer Surfaces
K 3 Surfaces
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The (-1 )-involution on the Jacobian Jr of an arbitrary Riemann surfacer of genus two leads to a singular surface, the Kummer surface Icr of Jr, which,after desingularization, defines a X-3 surface Kr . We consider ample line bundleson Kr coming from the even or odd sections of [n O] with prescribed vanishingat the 2-division points of Jr (0 is the theta divisor of Jr). We use an integrablesystem to show that in the cases we study the linear system is base-point-free,to determine which curves are contracted to singular points and to compute anexplicit equation for the surface in projective space. Our explicit methods applyto the Kummer surface of any Abelian surface, given as the fiber of the momentmap of an algebraic completely integrable system.
Fil: Piovan, Luis Amadeo. Universidad Nacional del Sur; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Vanhaecke, Pol. Université de Poitiers; Francia
description The (-1 )-involution on the Jacobian Jr of an arbitrary Riemann surfacer of genus two leads to a singular surface, the Kummer surface Icr of Jr, which,after desingularization, defines a X-3 surface Kr . We consider ample line bundleson Kr coming from the even or odd sections of [n O] with prescribed vanishingat the 2-division points of Jr (0 is the theta divisor of Jr). We use an integrablesystem to show that in the cases we study the linear system is base-point-free,to determine which curves are contracted to singular points and to compute anexplicit equation for the surface in projective space. Our explicit methods applyto the Kummer surface of any Abelian surface, given as the fiber of the momentmap of an algebraic completely integrable system.
publishDate 2000
dc.date.none.fl_str_mv 2000-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/80939
Piovan, Luis Amadeo; Vanhaecke, Pol; Integrable Systems and projective images of Kummer surfaces; Scuola Normale Superiore; Annali Della Scuola Normale Superiore Di Pisa Cl. Di Scienze - Iv; XXIX; 2; 10-2000; 351-392
0391-173X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/80939
identifier_str_mv Piovan, Luis Amadeo; Vanhaecke, Pol; Integrable Systems and projective images of Kummer surfaces; Scuola Normale Superiore; Annali Della Scuola Normale Superiore Di Pisa Cl. Di Scienze - Iv; XXIX; 2; 10-2000; 351-392
0391-173X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.numdam.org/article/ASNSP_2000_4_29_2_351_0.pdf
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Scuola Normale Superiore
publisher.none.fl_str_mv Scuola Normale Superiore
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.22299

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