Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands

This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of the Bernstein–Sato polynomial for a direct summand of a polynomial over a field...

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Detalles Bibliográficos
Autores: Álvarez Montaner, Josep|||0000-0001-6793-368X, Jeffries, Jack, Núñez-Betancourt, Luis
Tipo de recurso: informe técnico
Fecha de publicación:2019
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/341752
Acceso en línea:https://hdl.handle.net/2117/341752
Access Level:acceso abierto
Palabra clave:Commutative algebra
Àlgebra commutativa
Classificació AMS::14 Algebraic geometry::14F (Co)homology theory
Classificació AMS::13 Commutative rings and algebras::13N Differential algebra
Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions
Àrees temàtiques de la UPC::Matemàtiques i estadística
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spelling Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summandsÁlvarez Montaner, Josep|||0000-0001-6793-368XJeffries, JackNúñez-Betancourt, LuisCommutative algebraÀlgebra commutativaClassificació AMS::14 Algebraic geometry::14F (Co)homology theoryClassificació AMS::13 Commutative rings and algebras::13N Differential algebraClassificació AMS::13 Commutative rings and algebras::13A General commutative ring theoryClassificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructionsÀrees temàtiques de la UPC::Matemàtiques i estadísticaThis paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of the Bernstein–Sato polynomial for a direct summand of a polynomial over a field is proved in this context. It is observed that this polynomial can have zero as a root, or even positive roots. Moreover, a theory of V -filtrations is introduced for nonregular rings, and the existence of these objects is established for what we call differentially extensible summands. This family of rings includes toric, determinantal, and other invariant rings. This new theory is applied to the study of multiplier ideals and Hodge ideals of singular varieties. Finally, we extend known relations among the objects of interest in the smooth case to the setting of singular direct summands of polynomial rings.20192019-01-0120212021-03-16reporthttp://purl.org/coar/resource_type/c_93fcAOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/reportapplication/pdfhttps://hdl.handle.net/2117/341752reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3417522026-05-27T15:37:01Z
dc.title.none.fl_str_mv Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
title Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
spellingShingle Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
Álvarez Montaner, Josep|||0000-0001-6793-368X
Commutative algebra
Àlgebra commutativa
Classificació AMS::14 Algebraic geometry::14F (Co)homology theory
Classificació AMS::13 Commutative rings and algebras::13N Differential algebra
Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions
Àrees temàtiques de la UPC::Matemàtiques i estadística
title_short Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
title_full Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
title_fullStr Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
title_full_unstemmed Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
title_sort Bernstein-Sato functional equations, V-filtrations, and multiplier ideals of direct summands
dc.creator.none.fl_str_mv Álvarez Montaner, Josep|||0000-0001-6793-368X
Jeffries, Jack
Núñez-Betancourt, Luis
author Álvarez Montaner, Josep|||0000-0001-6793-368X
author_facet Álvarez Montaner, Josep|||0000-0001-6793-368X
Jeffries, Jack
Núñez-Betancourt, Luis
author_role author
author2 Jeffries, Jack
Núñez-Betancourt, Luis
author2_role author
author
dc.subject.none.fl_str_mv Commutative algebra
Àlgebra commutativa
Classificació AMS::14 Algebraic geometry::14F (Co)homology theory
Classificació AMS::13 Commutative rings and algebras::13N Differential algebra
Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions
Àrees temàtiques de la UPC::Matemàtiques i estadística
topic Commutative algebra
Àlgebra commutativa
Classificació AMS::14 Algebraic geometry::14F (Co)homology theory
Classificació AMS::13 Commutative rings and algebras::13N Differential algebra
Classificació AMS::13 Commutative rings and algebras::13A General commutative ring theory
Classificació AMS::16 Associative rings and algebras::16S Rings and algebras arising under various constructions
Àrees temàtiques de la UPC::Matemàtiques i estadística
description This paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct D-modules in which such formal equations can be studied. The existence of the Bernstein–Sato polynomial for a direct summand of a polynomial over a field is proved in this context. It is observed that this polynomial can have zero as a root, or even positive roots. Moreover, a theory of V -filtrations is introduced for nonregular rings, and the existence of these objects is established for what we call differentially extensible summands. This family of rings includes toric, determinantal, and other invariant rings. This new theory is applied to the study of multiplier ideals and Hodge ideals of singular varieties. Finally, we extend known relations among the objects of interest in the smooth case to the setting of singular direct summands of polynomial rings.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-01-01
2021
2021-03-16
dc.type.none.fl_str_mv report
http://purl.org/coar/resource_type/c_93fc
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/report
format report
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/341752
url https://hdl.handle.net/2117/341752
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
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
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.300724

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