The addition on Jacobian varieties from a geometric viewpoint

We give a geometric interpretation of the group law for Jacobian varieties by extending the geometric construction of chords and tangents on an elliptic curve. For any given algebraic curve $\mathcal{X}$ and reduced divisors $D_1, D_2 \in \mbox{Jac } \mathcal X$,wedefinecurves$\mathcal X^\prime$and$\mathcal X^{“}$suchthattheintersection$\mathcal X \cap \mathcal X^\prime$determinespreciselythedivisor$-(D_1+D_2)$andtheintersection$\mathcal X\cap \mathcal X^{”}$determines$D_1+D_2$. For superelliptic curves such formulas are made explicit.