A case study in bigraded commutative algebra

Autores
Cox, David; Dickenstein, Alicia Marcela; Schenk, Hal
Año de publicación
2007
Idioma
inglés
Tipo de recurso
parte de libro
Estado
versión publicada
Descripción
We study the commutative algebra of three bihomogeneous polynomials p_0,p_1,p_2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P^1 x P^1. Unlike the situation for P^2, the Koszul complex of the p_i is never exact. The purpose of this article is to illustrate how bigraded commutative algebra differs from the classical graded case and to indicate some of the theoretical tools needed to understand the free resolution of the ideal generated by p_0,p_1,p_2.
Fil: Cox, David. Amherst College. Department of Mathematics and Computer Science; Estados Unidos
Fil: Dickenstein, Alicia Marcela. 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
Fil: Schenk, Hal. Texas A&M University; Estados Unidos
Materia
bihomogeneous polynomials
syzygies
free resolutions
Koszul complex
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:11336/127516
Acceder
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network_name_str CONICET Digital (CONICET)
spelling A case study in bigraded commutative algebraCox, DavidDickenstein, Alicia MarcelaSchenk, Halbihomogeneous polynomialssyzygiesfree resolutionsKoszul complexhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We study the commutative algebra of three bihomogeneous polynomials p_0,p_1,p_2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P^1 x P^1. Unlike the situation for P^2, the Koszul complex of the p_i is never exact. The purpose of this article is to illustrate how bigraded commutative algebra differs from the classical graded case and to indicate some of the theoretical tools needed to understand the free resolution of the ideal generated by p_0,p_1,p_2.Fil: Cox, David. Amherst College. Department of Mathematics and Computer Science; Estados UnidosFil: Dickenstein, Alicia Marcela. 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"; ArgentinaFil: Schenk, Hal. Texas A&M University; Estados UnidosChapman and HallPeeva, Irena2007info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/bookParthttp://purl.org/coar/resource_type/c_3248info:ar-repo/semantics/parteDeLibroapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/127516Cox, David; Dickenstein, Alicia Marcela; Schenk, Hal; A case study in bigraded commutative algebra; Chapman and Hall; 2007; 67-1119780429147876CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/math/0409462info:eu-repo/semantics/altIdentifier/url/https://www.taylorfrancis.com/chapters/case-study-bigraded-commutative-algebra-david-cox-alicia-dickenstein-hal-schenck/e/10.1201/9781420050912-6info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T11:46:13Zoai:ri.conicet.gov.ar:11336/127516instacron: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 11:46:14.231CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A case study in bigraded commutative algebra
title A case study in bigraded commutative algebra
spellingShingle A case study in bigraded commutative algebra
Cox, David
bihomogeneous polynomials
syzygies
free resolutions
Koszul complex
title_short A case study in bigraded commutative algebra
title_full A case study in bigraded commutative algebra
title_fullStr A case study in bigraded commutative algebra
title_full_unstemmed A case study in bigraded commutative algebra
title_sort A case study in bigraded commutative algebra
dc.creator.none.fl_str_mv Cox, David
Dickenstein, Alicia Marcela
Schenk, Hal
author Cox, David
author_facet Cox, David
Dickenstein, Alicia Marcela
Schenk, Hal
author_role author
author2 Dickenstein, Alicia Marcela
Schenk, Hal
author2_role author
author
dc.contributor.none.fl_str_mv Peeva, Irena
dc.subject.none.fl_str_mv bihomogeneous polynomials
syzygies
free resolutions
Koszul complex
topic bihomogeneous polynomials
syzygies
free resolutions
Koszul complex
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 study the commutative algebra of three bihomogeneous polynomials p_0,p_1,p_2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P^1 x P^1. Unlike the situation for P^2, the Koszul complex of the p_i is never exact. The purpose of this article is to illustrate how bigraded commutative algebra differs from the classical graded case and to indicate some of the theoretical tools needed to understand the free resolution of the ideal generated by p_0,p_1,p_2.
Fil: Cox, David. Amherst College. Department of Mathematics and Computer Science; Estados Unidos
Fil: Dickenstein, Alicia Marcela. 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
Fil: Schenk, Hal. Texas A&M University; Estados Unidos
description We study the commutative algebra of three bihomogeneous polynomials p_0,p_1,p_2 of degree (2,1) in variables x,y;z,w, assuming that they never vanish simultaneously on P^1 x P^1. Unlike the situation for P^2, the Koszul complex of the p_i is never exact. The purpose of this article is to illustrate how bigraded commutative algebra differs from the classical graded case and to indicate some of the theoretical tools needed to understand the free resolution of the ideal generated by p_0,p_1,p_2.
publishDate 2007
dc.date.none.fl_str_mv 2007
dc.type.none.fl_str_mv info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/bookPart
http://purl.org/coar/resource_type/c_3248
info:ar-repo/semantics/parteDeLibro
status_str publishedVersion
format bookPart
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/127516
Cox, David; Dickenstein, Alicia Marcela; Schenk, Hal; A case study in bigraded commutative algebra; Chapman and Hall; 2007; 67-111
9780429147876
CONICET Digital
CONICET
url http://hdl.handle.net/11336/127516
identifier_str_mv Cox, David; Dickenstein, Alicia Marcela; Schenk, Hal; A case study in bigraded commutative algebra; Chapman and Hall; 2007; 67-111
9780429147876
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://arxiv.org/abs/math/0409462
info:eu-repo/semantics/altIdentifier/url/https://www.taylorfrancis.com/chapters/case-study-bigraded-commutative-algebra-david-cox-alicia-dickenstein-hal-schenck/e/10.1201/9781420050912-6
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 Chapman and Hall
publisher.none.fl_str_mv Chapman and Hall
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_ 1846782163350978560
score 12.982451

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