Algebraic construction of the Jacobian of a hyperelliptic curve

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


Let’s recall that a hyperelliptic curve C is determined by an equation s2 = f(t), where f is a polynomial of degree 2g+1; C has one point at infinity, and (t) = 2 · ∞
$$ \left( s \right)_\infty = \left( {2g + 1} \right) \cdot \infty . $$
We shall study the structure of Pic C = {group of divisors modulo linear equivalence}.


Branch Point Abelian Variety Discrete Subgroup Hyperelliptic Curve 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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