Tying together the analytic Jacobian and algebraic Jacobian

  • David Mumford
Part of the Modern Birkhäuser Classics book series (MBC)


So far in this Chapter, we have defined an algebraic variety Jac C and studied its invariant flows. In Chapter II, we associated to any compact Riemann Surface C a complex torus Jac C. If C is hyperelliptic so that both constructions apply, they are isomorphic by Abel’s theorem. We would now like to make this isomorphism explicitly, i.e., express the algebraic coordinates on Jac C-θ as theta functions.


Vector Field Meromorphic Function Theta Function Compact Riemann Surface Divisor Class 
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Copyright information

© Birkhäuser Boston 2007

Authors and Affiliations

  • David Mumford
    • 1
  1. 1.Division of Applied MathematicsBrown UniversityProvidenceUSA

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