Two-dimensional Riemann problem for rigid representations on an elliptic curve

We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fund...

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Detalles Bibliográficos
Autores: Matveeva, Anastasiia, Poberezhnyi, Vladimir Andreevich
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/370855
Acceso en línea:https://hdl.handle.net/2117/370855
https://dx.doi.org/10.1016/j.geomphys.2016.12.003
Access Level:acceso abierto
Palabra clave:Functions of complex variables
Elliptic curve
MonodromyRiemann–Hilbert problem
Logarithmic connection
Funcions de variables complexes
Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa
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spelling Two-dimensional Riemann problem for rigid representations on an elliptic curveMatveeva, AnastasiiaPoberezhnyi, Vladimir AndreevichFunctions of complex variablesElliptic curveMonodromyRiemann–Hilbert problemLogarithmic connectionFuncions de variables complexesClassificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domainÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexaWe consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along -cycle is trivial and monodromy along -cycle belong to certain orbit.This work has been funded by the Russian Academic Excellence Project ‘5-100’. The results of Section 2 have been obtained under support of the RSF grant 16-11-10160. Research has also been supported by the RFBR grant 17-01-00585.Peer Reviewed20172017-04-0120222022-07-22journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/370855https://dx.doi.org/10.1016/j.geomphys.2016.12.003reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3708552026-05-27T15:37:01Z
dc.title.none.fl_str_mv Two-dimensional Riemann problem for rigid representations on an elliptic curve
title Two-dimensional Riemann problem for rigid representations on an elliptic curve
spellingShingle Two-dimensional Riemann problem for rigid representations on an elliptic curve
Matveeva, Anastasiia
Functions of complex variables
Elliptic curve
MonodromyRiemann–Hilbert problem
Logarithmic connection
Funcions de variables complexes
Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa
title_short Two-dimensional Riemann problem for rigid representations on an elliptic curve
title_full Two-dimensional Riemann problem for rigid representations on an elliptic curve
title_fullStr Two-dimensional Riemann problem for rigid representations on an elliptic curve
title_full_unstemmed Two-dimensional Riemann problem for rigid representations on an elliptic curve
title_sort Two-dimensional Riemann problem for rigid representations on an elliptic curve
dc.creator.none.fl_str_mv Matveeva, Anastasiia
Poberezhnyi, Vladimir Andreevich
author Matveeva, Anastasiia
author_facet Matveeva, Anastasiia
Poberezhnyi, Vladimir Andreevich
author_role author
author2 Poberezhnyi, Vladimir Andreevich
author2_role author
dc.subject.none.fl_str_mv Functions of complex variables
Elliptic curve
MonodromyRiemann–Hilbert problem
Logarithmic connection
Funcions de variables complexes
Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa
topic Functions of complex variables
Elliptic curve
MonodromyRiemann–Hilbert problem
Logarithmic connection
Funcions de variables complexes
Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa
description We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along -cycle is trivial and monodromy along -cycle belong to certain orbit.
publishDate 2017
dc.date.none.fl_str_mv 2017
2017-04-01
2022
2022-07-22
dc.type.none.fl_str_mv journal 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://hdl.handle.net/2117/370855
https://dx.doi.org/10.1016/j.geomphys.2016.12.003
url https://hdl.handle.net/2117/370855
https://dx.doi.org/10.1016/j.geomphys.2016.12.003
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
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
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.301603

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