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Monodromy and normal forms

  • Fabrizio Catanese
Chapter

Abstract

We discuss the history of the monodromy theorem, starting from Weierstraß, and the concept of a monodromy group. From this viewpoint we compare then the Weierstraß, the Legendre and other normal forms for elliptic curves, explaining their geometric meaning and distinguishing them by their stabilizer in ℙSL(2, ℤ) and their monodromy. Then we focus on the birth of the concept of the Jacobian variety, and the geometrization of the theory of Abelian functions and integrals. We end illustrating the methods of complex analysis in the simplest issue, the difference equation f(z) = g(z + 1) - g(z) on ℂ.

Keywords

Normal Form Analytic Continuation Meromorphic Function Elliptic Curve Elliptic Curf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Fachmedien Wiesbaden 2016

Authors and Affiliations

  • Fabrizio Catanese
    • 1
  1. 1.Mathematisches InstitutUniversität BayreuthBayreuthGermany

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