Geodesic
Cubic differential forms and the group law on the Jacobian of a real algebraic curve
Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 597-604

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In an earlier paper [6], we gave an explicit geometric description of the group law on the neutral component of the set of real points of the Jacobian of a smooth quartic curve. Here, we generalize this description to curves of higher genus. We get a description of the group law on the neutral component of the set of real points of the Jacobian of a smooth curve in terms of cubic differential forms. When applied to canonical curves, one gets an explicit geometric description of this group law by intersecting the curve with cubic hypersurfaces. 
@article{BUMI_2003_8_6B_3_a6,
     author = {Huisman, J.},
     title = {Cubic differential forms and the group law on the {Jacobian} of a real algebraic curve},
     journal = {Bollettino della Unione matematica italiana},
     pages = {597--604},
     publisher = {mathdoc},
     volume = {Ser. 8, 6B},
     number = {3},
     year = {2003},
     zbl = {1112.14035},
     mrnumber = {MR2014821},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a6/}
}
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Huisman, J. Cubic differential forms and the group law on the Jacobian of a real algebraic curve. Bollettino della Unione matematica italiana, Série 8, 6B (2003) no. 3, pp. 597-604. http://geodesic.mathdoc.fr/item/BUMI_2003_8_6B_3_a6/