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
Descripción
Sumario: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.