  It is well-known that abelian varieties are projective, and so that there
exist explicit polynomial and rational functions which define both the variety
and its group law. It is however difficult to find any explicit polynomial and
rational functions describing these varieties or their group laws in dimensions
greater than two. One exception can be found in Mumford's classic "Lectures on
Theta", where he describes how to obtain an explicit model for hyperelliptic
Jacobians as the union of several affine pieces described as the vanishing
locus of explicit polynomial equations. In this article, we extend this work to
give explicit equations for the group law on a dense open set. One can view
these equations as generalizations of the usual chord-based group law on
elliptic curves.
