Periods of generalized Fermat curves |
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Authors: | Yerko Torres-Nova |
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Affiliation: | 1. Dipartimento di Scienza e Alta Tecnologia, Università degli Studi dell''Insubria, Via Valleggio 11, 22100 Como, Italy;2. Dipartimento di Matematica Federigo Enriques, Università degli Studi di Milano, Via Cesare Saldini 50, 20133 Milano, Italy;3. Dipartimento di Matematica, Università degli Studi di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy;1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain;2. Department of Mathematics, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussel, Belgium;3. Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland;1. Hong Kong University of Science and Technology, Hong Kong;2. University of Southern California, United States of America |
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Abstract: | Let be integers. A generalized Fermat curve of type is a compact Riemann surface S that admits a subgroup of conformal automorphisms isomorphic to , such that the quotient surface is biholomorphic to the Riemann sphere and has branch points, each one of order k. There exists a good algebraic model for these objects, which makes them easier to study. Using tools from algebraic topology and integration theory on Riemann surfaces, we find a set of generators for the first homology group of a generalized Fermat curve. Finally, with this information, we find a set of generators for the period lattice of the associated Jacobian variety. |
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Keywords: | Complex Geometry Riemann Surfaces Jacobian Variety Generalized Fermat Curve |
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