Codimension one distributions and stable rank 2 reflexive sheaves on threefolds
Autor(a) principal: | |
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Data de Publicação: | 2021 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Anais da Academia Brasileira de Ciências (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600301 |
Resumo: | Abstract % We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are then applied to the characterization of certain irreducible components of the moduli space of stable rank 2 reflexive sheaves on $\p3$, and to the construction of stable rank 2 reflexive sheaves with prescribed Chern classes on general threefolds. We also prove that if $\sG$ is a subfoliation of a codimension one distribution $\sF$ with isolated singularities, then $\sing(\sG)$ is a curve. As a consequence, we give a criterion to decide whether $\sG$ is globally given as the intersection of $\sF$ with another codimension one distribution. Turning our attention to codimension one distributions with non isolated singularities, we determine the number of connected components of the pure 1-dimensional component of the singular scheme. |
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Codimension one distributions and stable rank 2 reflexive sheaves on threefoldsdistributionsfoliationsreflexive sheavesmoduli spacesAbstract % We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are then applied to the characterization of certain irreducible components of the moduli space of stable rank 2 reflexive sheaves on $\p3$, and to the construction of stable rank 2 reflexive sheaves with prescribed Chern classes on general threefolds. We also prove that if $\sG$ is a subfoliation of a codimension one distribution $\sF$ with isolated singularities, then $\sing(\sG)$ is a curve. As a consequence, we give a criterion to decide whether $\sG$ is globally given as the intersection of $\sF$ with another codimension one distribution. Turning our attention to codimension one distributions with non isolated singularities, we determine the number of connected components of the pure 1-dimensional component of the singular scheme.Academia Brasileira de Ciências2021-01-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600301Anais da Academia Brasileira de Ciências v.93 suppl.3 2021reponame:Anais da Academia Brasileira de Ciências (Online)instname:Academia Brasileira de Ciências (ABC)instacron:ABC10.1590/0001-3765202120190909info:eu-repo/semantics/openAccessCALVO-ANDRADE,OMEGARCORRÊA,MAURÍCIOJARDIM,MARCOSeng2021-08-26T00:00:00Zoai:scielo:S0001-37652021000600301Revistahttp://www.scielo.br/aabchttps://old.scielo.br/oai/scielo-oai.php||aabc@abc.org.br1678-26900001-3765opendoar:2021-08-26T00:00Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC)false |
dc.title.none.fl_str_mv |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
title |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
spellingShingle |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds CALVO-ANDRADE,OMEGAR distributions foliations reflexive sheaves moduli spaces |
title_short |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
title_full |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
title_fullStr |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
title_full_unstemmed |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
title_sort |
Codimension one distributions and stable rank 2 reflexive sheaves on threefolds |
author |
CALVO-ANDRADE,OMEGAR |
author_facet |
CALVO-ANDRADE,OMEGAR CORRÊA,MAURÍCIO JARDIM,MARCOS |
author_role |
author |
author2 |
CORRÊA,MAURÍCIO JARDIM,MARCOS |
author2_role |
author author |
dc.contributor.author.fl_str_mv |
CALVO-ANDRADE,OMEGAR CORRÊA,MAURÍCIO JARDIM,MARCOS |
dc.subject.por.fl_str_mv |
distributions foliations reflexive sheaves moduli spaces |
topic |
distributions foliations reflexive sheaves moduli spaces |
description |
Abstract % We show that codimension one distributions with at most isolated singularities on certain smooth projective threefolds with Picard rank one have stable tangent sheaves. The ideas in the proof of this fact are then applied to the characterization of certain irreducible components of the moduli space of stable rank 2 reflexive sheaves on $\p3$, and to the construction of stable rank 2 reflexive sheaves with prescribed Chern classes on general threefolds. We also prove that if $\sG$ is a subfoliation of a codimension one distribution $\sF$ with isolated singularities, then $\sing(\sG)$ is a curve. As a consequence, we give a criterion to decide whether $\sG$ is globally given as the intersection of $\sF$ with another codimension one distribution. Turning our attention to codimension one distributions with non isolated singularities, we determine the number of connected components of the pure 1-dimensional component of the singular scheme. |
publishDate |
2021 |
dc.date.none.fl_str_mv |
2021-01-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600301 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652021000600301 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/0001-3765202120190909 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Academia Brasileira de Ciências |
publisher.none.fl_str_mv |
Academia Brasileira de Ciências |
dc.source.none.fl_str_mv |
Anais da Academia Brasileira de Ciências v.93 suppl.3 2021 reponame:Anais da Academia Brasileira de Ciências (Online) instname:Academia Brasileira de Ciências (ABC) instacron:ABC |
instname_str |
Academia Brasileira de Ciências (ABC) |
instacron_str |
ABC |
institution |
ABC |
reponame_str |
Anais da Academia Brasileira de Ciências (Online) |
collection |
Anais da Academia Brasileira de Ciências (Online) |
repository.name.fl_str_mv |
Anais da Academia Brasileira de Ciências (Online) - Academia Brasileira de Ciências (ABC) |
repository.mail.fl_str_mv |
||aabc@abc.org.br |
_version_ |
1754302870518235136 |