= Abel-Jacobi map of a compact Riemann surface
{c}
{title2=$\operatorname{AJ}:C^{(d)}\to H^0(C,K_C)^\vee/H_1(C,\mathbb Z)$}
Integration of <holomorphic differential forms> along cycles embeds the first <homology group> as a full <Euclidean lattice> in $H^0(C,K_C)^\vee$. Fixing a base point, sum the path integrals to the points of an effective <complex analytic divisor>. Different path choices differ by that lattice. The <Abel theorem for divisors> identifies the fibres with <linear equivalence of divisors>.
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