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Reference.org
Abel–Jacobi map
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Abel–Jacobi map is a construction of <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a> which relates an <a href="/facts/Algebraic_curve/LnWsPmDP">algebraic curve</a> to its <a href="/facts/Jacobian_variety/HFedCxIn">Jacobian variety</a>. In <a href="/facts/Riemannian_geometry/pPEzjyQC">Riemannian geometry</a>, it is a more general construction mapping a <a href="/facts/Manifold/rXPERJtu">manifold</a> to its Jacobi torus. The name derives from the theorem of <a href="/facts/Niels_Henrik_Abel/6kMfdRkT">Abel</a> and <a href="/facts/Carl_Gustav_Jacob_Jacobi/4Syeauo5">Jacobi</a> that two <a href="/facts/Effective_divisor/V0QDypeo">effective divisors</a> are <a href="/facts/Linearly_equivalent/V0QDypeo">linearly equivalent</a> if and only if they are indistinguishable under the Abel–Jacobi map. </p>