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We show that any Fermat hypercubic is apolar to a trigonal curve, and vice versa. We show also that the Waring number of the polar hypercubic associated to a tetragonal curve of genus  g  is at most⌈    3  2   g  ‐      7  2    ⌉    , and for a large class of them is at most4  3   g     ‐     3   .

Gonality, apolarity and hypercubics