Waring loci and the Strassen conjecture

Enrico Carlini (1) , Maria Virginia Catalisano (2) , Alessandro Oneto (3)

1 Polito - Politecnico di Torino = Polytechnic of Turin
2 DIPTEM - Dipartimento di Ingegneria della produzione, termoenergetica e modelli matematici
3 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

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.

Mots clés: homogeneous polynomials; symmetric tensors; Tensor decompositions; Waring problems; Waring loci

Domaines: Géométrie algébrique [math.AG]; Algèbre commutative [math.AC]

Enrico Carlini, Maria Virginia Catalisano, Alessandro Oneto. Waring loci and the Strassen conjecture. Advances in Mathematics, 2017, 314, pp.630 -- 662. ⟨10.1016/j.aim.2017.05.008⟩. ⟨hal-01589890⟩