On the uniformization of algebraic curves TeX Export

@article{citeulike:3211824, abstract = {Based 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.}, archivePrefix = {arXiv}, author = {Brezhnev, Yurii V.}, citeulike-article-id = {3211824}, citeulike-linkout-0 = {http://arxiv.org/abs/math/0205261}, citeulike-linkout-1 = {http://arxiv.org/pdf/math/0205261}, day = {9}, eprint = {math/0205261}, keywords = {abelian\_integrals, algebraic\_geometry, linear\_systems, monodromy}, month = {Sep}, posted-at = {2008-09-10 11:26:32}, priority = {2}, title = {On the uniformization of algebraic curves}, url = {http://arxiv.org/abs/math/0205261}, year = {2008} }

TY - JOUR ID - citeulike:3211824 L3 - citeulike-article-id:3211824 N2 - Based 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. TI - On the uniformization of algebraic curves KW - abelian_integrals KW - algebraic_geometry KW - linear_systems KW - monodromy AU - Brezhnev, Yurii PY - 2008/Sep/09/ UR - http://arxiv.org/abs/math/0205261 ER -