Waring loci and the Strassen conjecture

Abstract

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 family 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.

minor modifications in the expositions; Proposition 3.8 rephrased; proof of Theorem 5.1 corrected

References in corpus (2)

• Sufficient conditions for Strassen's additivity conjecture
• Symmetric tensors: rank, Strassen's conjecture and e-computability

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• On Comon's and Strassen's conjectures
• The Waring rank of binary binomial forms
• Binary forms of suprageneric rank and the multiple root loci