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

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 associate...

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Bibliographic Details
Published inMediterranean journal of mathematics Vol. 17; no. 6
Main Authors Dimca, Alexandru, Sticlaru, Gabriel
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2020
Springer Nature B.V
Springer Verlag
Subjects
Combinatorial analysis
Curves
Hyperplanes
Hyperspaces
Mathematics
Mathematics and Statistics
Polynomials
Singularity (mathematics)
Tensors
Waring decomposition
32S22
Waring rank
Projective hypersurface
Hyperplane arrangement
Isolated singularity
Primary 14J70
Secondary 14B05
32S05
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Summary: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.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-020-01609-0