This is a follow-up to [this question][1] (and my answer thereto). Given an algebraic curve, is there a way to realize its Jacobian explicitly as a zero-set of a bunch of polynomials in $\mathbb{P}^n.$ I care most about the complex case, but all ground fields are of interest...


  [1]: https://mathoverflow.net/questions/213001/conditions-for-underlying-space-of-an-orbifold-bbb-tn-gamma-to-be-a-sphere/213282#213282