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Article Dans Une Revue Mediterranean Journal of Mathematics Année : 2020

Waring Rank of Symmetric Tensors, and Singularities of Some Projective Hypersurfaces

Résumé

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.

Dates et versions

hal-03531057 , version 1 (18-01-2022)

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Alexandru Dimca, Gabriel Sticlaru. Waring Rank of Symmetric Tensors, and Singularities of Some Projective Hypersurfaces. Mediterranean Journal of Mathematics, 2020, 17 (6), ⟨10.1007/s00009-020-01609-0⟩. ⟨hal-03531057⟩
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