ABSTRACT

Given an algebraic curve, we can form its Jacobian, namely the group of divisors of degree 0 modulo principal divisors. As we saw in Corollary 11.4, the Jacobian of an elliptic curve gives the same group as the elliptic curve. However, for other curves, we get something new. In this chapter, we discuss hyperelliptic curves, for which the theory can be carried out rather explicitly.