On the uniformization of algebraic curves

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dc.creatorBrezhnev, Yurii V.
dc.date2002-05-24
dc.date2008-09-09
dc.date.accessioned2026-07-07T10:01:28Z
dc.date.available2026-07-07T10:01:28Z
dc.descriptionBased on Burnside's parametrization of the algebraic curve $y^2=x^5-x$ we provide remaining attributes of its uniformization: Fuchsian equations and their solutions, accessory parameters, monodromies, conformal maps, fundamental polygons, etc. As a generalization, we construct the zero genus uniformization of arbitrary curves. For hyperelliptic curves all the objects of the theory are explicitly described. We consider a large number of examples and, briefly, applications: Abelian integrals, metrics of Poincare, differential equations of the Jacobi--Chazy and Picard--Fuchs type, and others.
dc.descriptionFinal version; 36 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/math/0205261
dc.identifierhttp://arxiv.org/abs/math/0205261
dc.identifierMoscow Math. Journ. (2008), v.8(2), 233-271
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168641
dc.subjectClassical Analysis and ODEs
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subject30F10; 30F35
dc.titleOn the uniformization of algebraic curves
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