On the jumping lines of bundles of logarithmic vector fields along plane curves

For a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle ThCi on P 2 whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacob...

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Detalles Bibliográficos
Autores: Dimca, Alexandru|||0000-0001-9679-9870, Sticlaru, Gabriel
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:225701
Acceso en línea:https://ddd.uab.cat/record/225701
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6422006
Access Level:acceso abierto
Palabra clave:Plane curve
Vector bundle
Stable bundle
Splitting type
Jumping line
Jacobian module
Logarithmic vector fields
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spelling On the jumping lines of bundles of logarithmic vector fields along plane curvesDimca, Alexandru|||0000-0001-9679-9870Sticlaru, GabrielPlane curveVector bundleStable bundleSplitting typeJumping lineJacobian moduleLogarithmic vector fieldsFor a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle ThCi on P 2 whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of f and with the Bourbaki ideal of the module of Jacobian syzygies of f. In particular, when the vector bundle ThCi is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne, and Hulek resurface in the study of this special class of rank two vector bundles. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/225701https://dx.doi.org/urn:doi:10.5565/PUBLMAT6422006reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2257012026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the jumping lines of bundles of logarithmic vector fields along plane curves
title On the jumping lines of bundles of logarithmic vector fields along plane curves
spellingShingle On the jumping lines of bundles of logarithmic vector fields along plane curves
Dimca, Alexandru|||0000-0001-9679-9870
Plane curve
Vector bundle
Stable bundle
Splitting type
Jumping line
Jacobian module
Logarithmic vector fields
title_short On the jumping lines of bundles of logarithmic vector fields along plane curves
title_full On the jumping lines of bundles of logarithmic vector fields along plane curves
title_fullStr On the jumping lines of bundles of logarithmic vector fields along plane curves
title_full_unstemmed On the jumping lines of bundles of logarithmic vector fields along plane curves
title_sort On the jumping lines of bundles of logarithmic vector fields along plane curves
dc.creator.none.fl_str_mv Dimca, Alexandru|||0000-0001-9679-9870
Sticlaru, Gabriel
author Dimca, Alexandru|||0000-0001-9679-9870
author_facet Dimca, Alexandru|||0000-0001-9679-9870
Sticlaru, Gabriel
author_role author
author2 Sticlaru, Gabriel
author2_role author
dc.subject.none.fl_str_mv Plane curve
Vector bundle
Stable bundle
Splitting type
Jumping line
Jacobian module
Logarithmic vector fields
topic Plane curve
Vector bundle
Stable bundle
Splitting type
Jumping line
Jacobian module
Logarithmic vector fields
description For a reduced curve C : f = 0 in the complex projective plane P 2 , we study the set of jumping lines for the rank two vector bundle ThCi on P 2 whose sections are the logarithmic vector fields along C. We point out the relations of these jumping lines with the Lefschetz type properties of the Jacobian module of f and with the Bourbaki ideal of the module of Jacobian syzygies of f. In particular, when the vector bundle ThCi is unstable, a line is a jumping line if and only if it meets the 0-dimensional subscheme defined by this Bourbaki ideal, a result going back to Schwarzenberger. Other classical general results by Barth, Hartshorne, and Hulek resurface in the study of this special class of rank two vector bundles.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/225701
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6422006
url https://ddd.uab.cat/record/225701
https://dx.doi.org/urn:doi:10.5565/PUBLMAT6422006
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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