Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1

Detalhes bibliográficos
Autor(a) principal: Mendes, S.
Data de Publicação: 2021
Outros Autores: Soares, H., Miró-Roig, M.
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10071/22539
Resumo: We find the complete integer solutions of the equation X2 + Y2 + Z2 − 4XY − 4YZ + 10XZ = 1. As an application, we prove that, for each solution (a, b, c) such that a > 0, b − 2a > 0 and (b − 2a)2 ≥ 4a, there is a vector bundle E on ℙ3 defined by a minimal linear resolution 0 → Oℙ3 (−2)a → Oℙ3 (−1)b → Oℙc3 → E → 0. In particular, E satisfies ?(End E) = 1.
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spelling Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1Homological dimensionLinear resolutionsDiophantine equationsTernary quadratic formsWe find the complete integer solutions of the equation X2 + Y2 + Z2 − 4XY − 4YZ + 10XZ = 1. As an application, we prove that, for each solution (a, b, c) such that a > 0, b − 2a > 0 and (b − 2a)2 ≥ 4a, there is a vector bundle E on ℙ3 defined by a minimal linear resolution 0 → Oℙ3 (−2)a → Oℙ3 (−1)b → Oℙc3 → E → 0. In particular, E satisfies ?(End E) = 1.Walter de Gruyter GmbH2022-04-07T00:00:00Z2021-01-01T00:00:00Z20212021-05-07T11:26:48Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10071/22539eng0933-774110.1515/forum-2020-0169Mendes, S.Soares, H.Miró-Roig, M.info: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:RCAAP2023-11-09T17:23:00Zoai:repositorio.iscte-iul.pt:10071/22539Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:10:34.616627Repositório 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 Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
title Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
spellingShingle Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
Mendes, S.
Homological dimension
Linear resolutions
Diophantine equations
Ternary quadratic forms
title_short Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
title_full Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
title_fullStr Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
title_full_unstemmed Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
title_sort Vector bundles E on P^3 with homological dimension 2 and chi(End E)=1
author Mendes, S.
author_facet Mendes, S.
Soares, H.
Miró-Roig, M.
author_role author
author2 Soares, H.
Miró-Roig, M.
author2_role author
author
dc.contributor.author.fl_str_mv Mendes, S.
Soares, H.
Miró-Roig, M.
dc.subject.por.fl_str_mv Homological dimension
Linear resolutions
Diophantine equations
Ternary quadratic forms
topic Homological dimension
Linear resolutions
Diophantine equations
Ternary quadratic forms
description We find the complete integer solutions of the equation X2 + Y2 + Z2 − 4XY − 4YZ + 10XZ = 1. As an application, we prove that, for each solution (a, b, c) such that a > 0, b − 2a > 0 and (b − 2a)2 ≥ 4a, there is a vector bundle E on ℙ3 defined by a minimal linear resolution 0 → Oℙ3 (−2)a → Oℙ3 (−1)b → Oℙc3 → E → 0. In particular, E satisfies ?(End E) = 1.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01T00:00:00Z
2021
2021-05-07T11:26:48Z
2022-04-07T00:00:00Z
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/10071/22539
url http://hdl.handle.net/10071/22539
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0933-7741
10.1515/forum-2020-0169
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Walter de Gruyter GmbH
publisher.none.fl_str_mv Walter de Gruyter GmbH
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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