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We give a detailed proof for Gordan-Noether’s results in “Ueber die algebraischen Formen, deren Hesse’sche Determinante identisch verschwindet.” C. Lossen has written a paper in a similar direction as the present paper. However, our paper is independent of Lossen’s paper and includes a considerable number of new observations.

On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version)