Complex Curves

  • Jeremy Gray
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


Bezout’s theorem, that curves of degrees k and m meet in km points, forces geometers to allow complex points on a curve, but despite this incentive the step to admit complex algebraic curves was resisted until Riemann’s work in the 1850s. An important stimulus was the study of elliptic integrals, which are necessarily complex.


Riemann Surface Elliptic Function Elliptic Integral Modern Mathematician Complex Point 
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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe Open UniversityWalton Hall, Milton KeynesUnited Kingdom
  2. 2.The Mathematics InstituteThe University of WarwickWarwickUnited Kingdom

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