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Algebraic construction of the Jacobian of a hyperelliptic curve

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

Abstract

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}.

Keywords

Branch Point Abelian Variety Discrete Subgroup Hyperelliptic Curve 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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