Splitting criteria for vector bundles on the symplectic isotropic Grassmannian
Autor(a) principal: | |
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Data de Publicação: | 2009 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10174/2503 |
Resumo: | We extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic isotropic lines. For the general case the generalization of Ottaviani's conditions are sufficient for vector bundles over the symplectic isotropic Grassmannian. By a calculation in the program LiE, we find that Ottaviani's conditions are necessary for Lagrangian Grassmannian of isotropic $k$-planes for k<7, but they fail to be necessary for the case of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a related set of necessary and sufficient splitting criteria for the Lagrangian Grassmannian. |
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Splitting criteria for vector bundles on the symplectic isotropic Grassmanniangeometria algébricafibrados vectoriaisgrassmanianoWe extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic isotropic lines. For the general case the generalization of Ottaviani's conditions are sufficient for vector bundles over the symplectic isotropic Grassmannian. By a calculation in the program LiE, we find that Ottaviani's conditions are necessary for Lagrangian Grassmannian of isotropic $k$-planes for k<7, but they fail to be necessary for the case of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a related set of necessary and sufficient splitting criteria for the Lagrangian Grassmannian.Dipartimento di Matematica e Informatica, Università degli Studi di Catania2011-01-25T09:28:59Z2011-01-252009-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article232557 bytesapplication/pdfhttp://hdl.handle.net/10174/2503http://hdl.handle.net/10174/2503engpáginas155-1760373-35052Le Matematiche (Catania)64livrepmm@uevora.ptoeding@math.unifi.itGiuffrida, SalvatoreCantone, DomenicoDi Fazio, GiuseppeMuscato, OrazioQuattrocchi, GaetanoRusso, GiovanniMaggioni, Renato606Macias Marques, PedroOeding, Lukeinfo: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:RCAAP2024-01-03T18:39:03Zoai:dspace.uevora.pt:10174/2503Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-20T00:58:12.516055Repositório 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 |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
title |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
spellingShingle |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian Macias Marques, Pedro geometria algébrica fibrados vectoriais grassmaniano |
title_short |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
title_full |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
title_fullStr |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
title_full_unstemmed |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
title_sort |
Splitting criteria for vector bundles on the symplectic isotropic Grassmannian |
author |
Macias Marques, Pedro |
author_facet |
Macias Marques, Pedro Oeding, Luke |
author_role |
author |
author2 |
Oeding, Luke |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Macias Marques, Pedro Oeding, Luke |
dc.subject.por.fl_str_mv |
geometria algébrica fibrados vectoriais grassmaniano |
topic |
geometria algébrica fibrados vectoriais grassmaniano |
description |
We extend a theorem of Ottaviani on cohomological splitting criterion for vector bundles over the Grassmannian to the case of the symplectic isotropic Grassmanian. We find necessary and sufficient conditions for the case of the Grassmanian of symplectic isotropic lines. For the general case the generalization of Ottaviani's conditions are sufficient for vector bundles over the symplectic isotropic Grassmannian. By a calculation in the program LiE, we find that Ottaviani's conditions are necessary for Lagrangian Grassmannian of isotropic $k$-planes for k<7, but they fail to be necessary for the case of the Lagrangian Grassmannian of isotropic 7-planes. Finally, we find a related set of necessary and sufficient splitting criteria for the Lagrangian Grassmannian. |
publishDate |
2009 |
dc.date.none.fl_str_mv |
2009-01-01T00:00:00Z 2011-01-25T09:28:59Z 2011-01-25 |
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/10174/2503 http://hdl.handle.net/10174/2503 |
url |
http://hdl.handle.net/10174/2503 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
páginas155-176 0373-3505 2 Le Matematiche (Catania) 64 livre pmm@uevora.pt oeding@math.unifi.it Giuffrida, Salvatore Cantone, Domenico Di Fazio, Giuseppe Muscato, Orazio Quattrocchi, Gaetano Russo, Giovanni Maggioni, Renato 606 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
232557 bytes application/pdf |
dc.publisher.none.fl_str_mv |
Dipartimento di Matematica e Informatica, Università degli Studi di Catania |
publisher.none.fl_str_mv |
Dipartimento di Matematica e Informatica, Università degli Studi di Catania |
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 |
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1799136465204019200 |