Waring loci and the Strassen conjecture

The Waring locus of a form F is the collection of the degree one forms appearing in some minimal sum of powers decomposition of F. In this paper, we give a complete description of Waring loci for several families of forms, such as quadrics, monomials, binary forms and plane cubics. We also introduce...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2017-07, Vol.314, p.630-662
Main Authors: Carlini, Enrico, Catalisano, Maria Virginia, Oneto, Alessandro
Format: Article
Language:English
Subjects:
Algebraic Geometry
Commutative Algebra
Mathematics
Strassen's conjecture
Symmetric tensors decomposition
Waring locus
Waring rank
Zero dimensional schemes
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Summary:The Waring locus of a form F is the collection of the degree one forms appearing in some minimal sum of powers decomposition of F. In this paper, we give a complete description of Waring loci for several families of forms, such as quadrics, monomials, binary forms and plane cubics. We also introduce a Waring loci version of Strassen's Conjecture, which implies the original conjecture, and we prove it in many cases.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2017.05.008