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              <p>We show that if a homogeneous polynomial f in n variables has Waring rank n + 1, then the corresponding projective hypersurface f = 0 has at most isolated singularities, and the type of these singularities is completely determined by the combinatorics of a hyperplane arrangement naturally associated with the Waring decomposition of f. We also discuss the relation between the Waring rank and the type of singularities on a plane curve, when this curve is defined by the suspension of a binary form, or when the Waring rank is 5.</p>
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