Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups

Detalhes bibliográficos
Autor(a) principal: Silva, Jaime
Data de Publicação: 2021
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.21/13580
Resumo: Let X be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products Sym(n) X when the cohomology of X is given by exterior products of cohomology classes with odd degree. We obtain an expression for the equivariant mixed Hodge polynomials mu(Sn)(Xn)(t, u, v), codifying the permutation action of S-n as well as its subgroups. This allows us to deduce formulas for the mixed Hodge polynomials of its symmetric products mu(Symn X) (t, u, v). These formulas are then applied to the case of linear algebraic groups.
id RCAP_b43c06ef7e696d29f754d30ca1d3eab1
oai_identifier_str oai:repositorio.ipl.pt:10400.21/13580
network_acronym_str RCAP
network_name_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository_id_str 7160
spelling Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groupsHodge structuresSym(n) XCohomologyHodge polynomialsLet X be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products Sym(n) X when the cohomology of X is given by exterior products of cohomology classes with odd degree. We obtain an expression for the equivariant mixed Hodge polynomials mu(Sn)(Xn)(t, u, v), codifying the permutation action of S-n as well as its subgroups. This allows us to deduce formulas for the mixed Hodge polynomials of its symmetric products mu(Symn X) (t, u, v). These formulas are then applied to the case of linear algebraic groups.SpringerRCIPLSilva, Jaime2021-07-26T14:18:29Z2021-072021-07-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.21/13580engSILVA, Jaime D. – Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups. Manuscripta Mathematica. ISSN 0025-2611. (2021), pp. 1-180025-261110.1007/s00229-021-01314-61432-1785metadata only accessinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-08-03T10:08:34Zoai:repositorio.ipl.pt:10400.21/13580Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:21:30.097239Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
title Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
spellingShingle Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
Silva, Jaime
Hodge structures
Sym(n) X
Cohomology
Hodge polynomials
title_short Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
title_full Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
title_fullStr Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
title_full_unstemmed Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
title_sort Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups
author Silva, Jaime
author_facet Silva, Jaime
author_role author
dc.contributor.none.fl_str_mv RCIPL
dc.contributor.author.fl_str_mv Silva, Jaime
dc.subject.por.fl_str_mv Hodge structures
Sym(n) X
Cohomology
Hodge polynomials
topic Hodge structures
Sym(n) X
Cohomology
Hodge polynomials
description Let X be a complex quasi-projective algebraic variety. In this paper we study the mixed Hodge structures of the symmetric products Sym(n) X when the cohomology of X is given by exterior products of cohomology classes with odd degree. We obtain an expression for the equivariant mixed Hodge polynomials mu(Sn)(Xn)(t, u, v), codifying the permutation action of S-n as well as its subgroups. This allows us to deduce formulas for the mixed Hodge polynomials of its symmetric products mu(Symn X) (t, u, v). These formulas are then applied to the case of linear algebraic groups.
publishDate 2021
dc.date.none.fl_str_mv 2021-07-26T14:18:29Z
2021-07
2021-07-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.21/13580
url http://hdl.handle.net/10400.21/13580
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv SILVA, Jaime D. – Equivariant Hodge-Deligne polynomials of symmetric products of algebraic groups. Manuscripta Mathematica. ISSN 0025-2611. (2021), pp. 1-18
0025-2611
10.1007/s00229-021-01314-6
1432-1785
dc.rights.driver.fl_str_mv metadata only access
info:eu-repo/semantics/openAccess
rights_invalid_str_mv metadata only access
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer
publisher.none.fl_str_mv Springer
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
_version_ 1799133486089502720

Registros relacionados