Waring loci and the Strassen conjecture
Algebraic Geometry
2019-02-07 v3 Commutative Algebra
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.
Keywords
Cite
@article{arxiv.1605.00384,
title = {Waring loci and the Strassen conjecture},
author = {Enrico Carlini and Maria Virginia Catalisano and Alessandro Oneto},
journal= {arXiv preprint arXiv:1605.00384},
year = {2019}
}
Comments
minor modifications in the expositions; Proposition 3.8 rephrased; proof of Theorem 5.1 corrected