Sparse Nullstellensatz, Resultants, and Determinants of Complexes

Autores
D Andrea, Carlos A; Jeronimo, Gabriela Tali
Año de publicación
2025
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We refine and extend a result by Tuitman on the supports of a Bézout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul-type complex.
Fil: D Andrea, Carlos A. Universidad de Barcelona; España
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
HILBERT'S NULLSTELLENSATZ
SPARSE RESULTANTS
DETERMINANTS OF COMPLEXES
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:11336/271061
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Sparse Nullstellensatz, Resultants, and Determinants of ComplexesD Andrea, Carlos AJeronimo, Gabriela TaliHILBERT'S NULLSTELLENSATZSPARSE RESULTANTSDETERMINANTS OF COMPLEXEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We refine and extend a result by Tuitman on the supports of a Bézout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul-type complex.Fil: D Andrea, Carlos A. Universidad de Barcelona; EspañaFil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaOxford University Press2025-06info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/271061D Andrea, Carlos A; Jeronimo, Gabriela Tali; Sparse Nullstellensatz, Resultants, and Determinants of Complexes; Oxford University Press; International Mathematics Research Notices; 2025; 12; 6-2025; 1-231073-7928CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2025/12/rnaf174/8171535?redirectedFrom=fulltextinfo:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnaf174info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2407.13450info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:04:20Zoai:ri.conicet.gov.ar:11336/271061instacron: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:34982025-09-29 10:04:20.579CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Sparse Nullstellensatz, Resultants, and Determinants of Complexes
title Sparse Nullstellensatz, Resultants, and Determinants of Complexes
spellingShingle Sparse Nullstellensatz, Resultants, and Determinants of Complexes
D Andrea, Carlos A
HILBERT'S NULLSTELLENSATZ
SPARSE RESULTANTS
DETERMINANTS OF COMPLEXES
title_short Sparse Nullstellensatz, Resultants, and Determinants of Complexes
title_full Sparse Nullstellensatz, Resultants, and Determinants of Complexes
title_fullStr Sparse Nullstellensatz, Resultants, and Determinants of Complexes
title_full_unstemmed Sparse Nullstellensatz, Resultants, and Determinants of Complexes
title_sort Sparse Nullstellensatz, Resultants, and Determinants of Complexes
dc.creator.none.fl_str_mv D Andrea, Carlos A
Jeronimo, Gabriela Tali
author D Andrea, Carlos A
author_facet D Andrea, Carlos A
Jeronimo, Gabriela Tali
author_role author
author2 Jeronimo, Gabriela Tali
author2_role author
dc.subject.none.fl_str_mv HILBERT'S NULLSTELLENSATZ
SPARSE RESULTANTS
DETERMINANTS OF COMPLEXES
topic HILBERT'S NULLSTELLENSATZ
SPARSE RESULTANTS
DETERMINANTS OF COMPLEXES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We refine and extend a result by Tuitman on the supports of a Bézout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul-type complex.
Fil: D Andrea, Carlos A. Universidad de Barcelona; España
Fil: Jeronimo, Gabriela Tali. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We refine and extend a result by Tuitman on the supports of a Bézout identity satisfied by a finite sequence of sparse Laurent polynomials without common zeroes in the toric variety associated to their supports. When the number of these polynomials is one more than the dimension of the ambient space, we obtain a formula for computing the sparse resultant as the determinant of a Koszul-type complex.
publishDate 2025
dc.date.none.fl_str_mv 2025-06
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/11336/271061
D Andrea, Carlos A; Jeronimo, Gabriela Tali; Sparse Nullstellensatz, Resultants, and Determinants of Complexes; Oxford University Press; International Mathematics Research Notices; 2025; 12; 6-2025; 1-23
1073-7928
CONICET Digital
CONICET
url http://hdl.handle.net/11336/271061
identifier_str_mv D Andrea, Carlos A; Jeronimo, Gabriela Tali; Sparse Nullstellensatz, Resultants, and Determinants of Complexes; Oxford University Press; International Mathematics Research Notices; 2025; 12; 6-2025; 1-23
1073-7928
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://academic.oup.com/imrn/article-abstract/2025/12/rnaf174/8171535?redirectedFrom=fulltext
info:eu-repo/semantics/altIdentifier/doi/10.1093/imrn/rnaf174
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/2407.13450
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
application/pdf
dc.publisher.none.fl_str_mv Oxford University Press
publisher.none.fl_str_mv Oxford University Press
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
_version_ 1844613868385468416
score 13.070432

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