Effective criteria for bigraded birational maps

Autores
Botbol, Nicolas Santiago; Busé, Laurent; Chardin, Marc; Hassanzadeh, Seyed Hamid; Simis, Aron; Tran, Quang Hoa
Año de publicación
2017
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper.
Fil: Botbol, Nicolas Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Busé, Laurent. Université Côte d'Azur; Francia
Fil: Chardin, Marc. Institut de Mathématiques de Jussieu; Francia
Fil: Hassanzadeh, Seyed Hamid. Universidade Federal do Rio de Janeiro; Brasil
Fil: Simis, Aron. Universidade Federal de Pernambuco; Brasil
Fil: Tran, Quang Hoa. Institut de Mathématiques de Jussieu; Francia. Hue University's College of Education; Francia
Materia
BIGRADED BASE IDEAL
BIGRADED RATIONAL MAPS
BIRATIONALITY CRITERIA
JACOBIAN DUAL RANK
REES ALGEBRAS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/60061
Acceder
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network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Effective criteria for bigraded birational mapsBotbol, Nicolas SantiagoBusé, LaurentChardin, MarcHassanzadeh, Seyed HamidSimis, AronTran, Quang HoaBIGRADED BASE IDEALBIGRADED RATIONAL MAPSBIRATIONALITY CRITERIAJACOBIAN DUAL RANKREES ALGEBRAShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper.Fil: Botbol, Nicolas Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Busé, Laurent. Université Côte d'Azur; FranciaFil: Chardin, Marc. Institut de Mathématiques de Jussieu; FranciaFil: Hassanzadeh, Seyed Hamid. Universidade Federal do Rio de Janeiro; BrasilFil: Simis, Aron. Universidade Federal de Pernambuco; BrasilFil: Tran, Quang Hoa. Institut de Mathématiques de Jussieu; Francia. Hue University's College of Education; FranciaAcademic Press Ltd - Elsevier Science Ltd2017-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/60061Botbol, Nicolas Santiago; Busé, Laurent; Chardin, Marc; Hassanzadeh, Seyed Hamid; Simis, Aron; et al.; Effective criteria for bigraded birational maps; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 81; 7-2017; 69-870747-7171CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2016.12.001info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717116301626info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1602.07490info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-nd/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:03:09Zoai:ri.conicet.gov.ar:11336/60061instacron: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:34982025-10-22 11:03:09.918CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Effective criteria for bigraded birational maps
title Effective criteria for bigraded birational maps
spellingShingle Effective criteria for bigraded birational maps
Botbol, Nicolas Santiago
BIGRADED BASE IDEAL
BIGRADED RATIONAL MAPS
BIRATIONALITY CRITERIA
JACOBIAN DUAL RANK
REES ALGEBRAS
title_short Effective criteria for bigraded birational maps
title_full Effective criteria for bigraded birational maps
title_fullStr Effective criteria for bigraded birational maps
title_full_unstemmed Effective criteria for bigraded birational maps
title_sort Effective criteria for bigraded birational maps
dc.creator.none.fl_str_mv Botbol, Nicolas Santiago
Busé, Laurent
Chardin, Marc
Hassanzadeh, Seyed Hamid
Simis, Aron
Tran, Quang Hoa
author Botbol, Nicolas Santiago
author_facet Botbol, Nicolas Santiago
Busé, Laurent
Chardin, Marc
Hassanzadeh, Seyed Hamid
Simis, Aron
Tran, Quang Hoa
author_role author
author2 Busé, Laurent
Chardin, Marc
Hassanzadeh, Seyed Hamid
Simis, Aron
Tran, Quang Hoa
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv BIGRADED BASE IDEAL
BIGRADED RATIONAL MAPS
BIRATIONALITY CRITERIA
JACOBIAN DUAL RANK
REES ALGEBRAS
topic BIGRADED BASE IDEAL
BIGRADED RATIONAL MAPS
BIRATIONALITY CRITERIA
JACOBIAN DUAL RANK
REES ALGEBRAS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper.
Fil: Botbol, Nicolas Santiago. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Busé, Laurent. Université Côte d'Azur; Francia
Fil: Chardin, Marc. Institut de Mathématiques de Jussieu; Francia
Fil: Hassanzadeh, Seyed Hamid. Universidade Federal do Rio de Janeiro; Brasil
Fil: Simis, Aron. Universidade Federal de Pernambuco; Brasil
Fil: Tran, Quang Hoa. Institut de Mathématiques de Jussieu; Francia. Hue University's College of Education; Francia
description In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper.
publishDate 2017
dc.date.none.fl_str_mv 2017-07
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/11336/60061
Botbol, Nicolas Santiago; Busé, Laurent; Chardin, Marc; Hassanzadeh, Seyed Hamid; Simis, Aron; et al.; Effective criteria for bigraded birational maps; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 81; 7-2017; 69-87
0747-7171
CONICET Digital
CONICET
url http://hdl.handle.net/11336/60061
identifier_str_mv Botbol, Nicolas Santiago; Busé, Laurent; Chardin, Marc; Hassanzadeh, Seyed Hamid; Simis, Aron; et al.; Effective criteria for bigraded birational maps; Academic Press Ltd - Elsevier Science Ltd; Journal Of Symbolic Computation; 81; 7-2017; 69-87
0747-7171
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.jsc.2016.12.001
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0747717116301626
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1602.07490
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
publisher.none.fl_str_mv Academic Press Ltd - Elsevier Science Ltd
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 12.982451

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