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Tying together the analytic Jacobian and algebraic Jacobian

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

Abstract

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.

Keywords

Vector Field Meromorphic Function Theta Function Compact Riemann Surface Divisor Class 
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

© Birkhäuser Boston 2007

Authors and Affiliations

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

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