Algebraic construction of the Jacobian of a hyperelliptic curve

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}.