Waring rank of symmetric tensors, and singularities of some projective hypersurfaces

2019/02/04 by Dimca, Alexandru, Sticlaru, Gabriel
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1902.01351

Abstract

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.

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• The symmetric geometric rank of symmetric tensors
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