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

descriptionPublicationkeyboard_double_arrow_right Article 01 Apr 2017 English Publisher:Elsevier BVJournal:Journal of Geometry and Physics, volume 114, pages 384-393 (issn: 0393-0440,

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Authors: Matveeva, Anastasiia; Poberezhnyi, Vladimir Andreevich;

doi: 10.1016/j.geomphys.2016.12.003

handle: 2117/370855

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

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Abstract

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. 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 Reviewed

Related Organizations

National Research University Higher School of Economics
Russian Federation
Universitat Politècnica de Catalunya
Spain
Universitat Polite`cnica de Catalunya
Spain

Keywords

Riemann-Hilbert problem, :Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa [Àrees temàtiques de la UPC], Funcions de variables complexes, :30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain [Classificació AMS], monodromy, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Funcions de variable complexa, Logarithmic connection, Classificació AMS::30 Functions of a complex variable::30E Miscellaneous topics of analysis in the complex domain, Functions of complex variables, logarithmic connection, MonodromyRiemann–Hilbert problem, Elliptic curve, Riemann-Hilbert problems in context of PDEs, Elliptic curves, elliptic curve

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