Quantum toric degeneration of quantum flag and Schubert varieties

Autores
Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber extend to all fibers. We then show that quantized coordinate rings of flag varieties and Schubert varieties can be filtered so that the associated graded rings are twisted semigroup rings in the sense of [RZ12]. This is a noncommutative version of the result due to Caldero [C02] stating that flag and Schubert varieties degenerate into toric varieties, and implies that quantized coordinate rings of flag and Schubert varieties are AS-Cohen–Macaulay.
Fil: Rigal, L.. Universite de Paris 13-Nord; Francia
Fil: Zadunaisky Bustillos, Pablo Mauricio. 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
NONCOMMUTATIVE GEOMETRY
DEFORMATIONS
QUANTUM FLAG
QUANTUM SCHUBERT
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:11336/143907
Acceder
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network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Quantum toric degeneration of quantum flag and Schubert varietiesRigal, L.Zadunaisky Bustillos, Pablo MauricioNONCOMMUTATIVE GEOMETRYDEFORMATIONSQUANTUM FLAGQUANTUM SCHUBERThttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber extend to all fibers. We then show that quantized coordinate rings of flag varieties and Schubert varieties can be filtered so that the associated graded rings are twisted semigroup rings in the sense of [RZ12]. This is a noncommutative version of the result due to Caldero [C02] stating that flag and Schubert varieties degenerate into toric varieties, and implies that quantized coordinate rings of flag and Schubert varieties are AS-Cohen–Macaulay.Fil: Rigal, L.. Universite de Paris 13-Nord; FranciaFil: Zadunaisky Bustillos, Pablo Mauricio. 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"; ArgentinaSpringer2020-09info: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/11336/143907Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum toric degeneration of quantum flag and Schubert varieties ; Springer; Transformation Groups; 26; 3; 9-2020; 1113-11431083-4362CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-020-09615-yinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-020-09615-yinfo:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07675info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:58:27Zoai:ri.conicet.gov.ar:11336/143907instacron: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:34982025-09-03 09:58:27.479CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Quantum toric degeneration of quantum flag and Schubert varieties
title Quantum toric degeneration of quantum flag and Schubert varieties
spellingShingle Quantum toric degeneration of quantum flag and Schubert varieties
Rigal, L.
NONCOMMUTATIVE GEOMETRY
DEFORMATIONS
QUANTUM FLAG
QUANTUM SCHUBERT
title_short Quantum toric degeneration of quantum flag and Schubert varieties
title_full Quantum toric degeneration of quantum flag and Schubert varieties
title_fullStr Quantum toric degeneration of quantum flag and Schubert varieties
title_full_unstemmed Quantum toric degeneration of quantum flag and Schubert varieties
title_sort Quantum toric degeneration of quantum flag and Schubert varieties
dc.creator.none.fl_str_mv Rigal, L.
Zadunaisky Bustillos, Pablo Mauricio
author Rigal, L.
author_facet Rigal, L.
Zadunaisky Bustillos, Pablo Mauricio
author_role author
author2 Zadunaisky Bustillos, Pablo Mauricio
author2_role author
dc.subject.none.fl_str_mv NONCOMMUTATIVE GEOMETRY
DEFORMATIONS
QUANTUM FLAG
QUANTUM SCHUBERT
topic NONCOMMUTATIVE GEOMETRY
DEFORMATIONS
QUANTUM FLAG
QUANTUM SCHUBERT
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 show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber extend to all fibers. We then show that quantized coordinate rings of flag varieties and Schubert varieties can be filtered so that the associated graded rings are twisted semigroup rings in the sense of [RZ12]. This is a noncommutative version of the result due to Caldero [C02] stating that flag and Schubert varieties degenerate into toric varieties, and implies that quantized coordinate rings of flag and Schubert varieties are AS-Cohen–Macaulay.
Fil: Rigal, L.. Universite de Paris 13-Nord; Francia
Fil: Zadunaisky Bustillos, Pablo Mauricio. 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 show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry, this can be seen as an analogue of the classical result that, in a flat family of varieties over the affine line, regularity properties of the exceptional fiber extend to all fibers. We then show that quantized coordinate rings of flag varieties and Schubert varieties can be filtered so that the associated graded rings are twisted semigroup rings in the sense of [RZ12]. This is a noncommutative version of the result due to Caldero [C02] stating that flag and Schubert varieties degenerate into toric varieties, and implies that quantized coordinate rings of flag and Schubert varieties are AS-Cohen–Macaulay.
publishDate 2020
dc.date.none.fl_str_mv 2020-09
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/11336/143907
Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum toric degeneration of quantum flag and Schubert varieties ; Springer; Transformation Groups; 26; 3; 9-2020; 1113-1143
1083-4362
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143907
identifier_str_mv Rigal, L.; Zadunaisky Bustillos, Pablo Mauricio; Quantum toric degeneration of quantum flag and Schubert varieties ; Springer; Transformation Groups; 26; 3; 9-2020; 1113-1143
1083-4362
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1007/s00031-020-09615-y
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007%2Fs00031-020-09615-y
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1902.07675
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 Springer
publisher.none.fl_str_mv Springer
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 13.13397

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