The symmetric geometric rank of symmetric tensors
-
Lindberg, Julia
[1]
;
Santarsiero, Pierpaola
[2]
-
[1] Georgia Institute of Technology
Georgia Institute of Technology
Estados Unidos
-
[2] University of Bologna
University of Bologna
Bolonia, Italia
-
- Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 3, 2026, págs. 791-813
- Idioma: inglés
- Enlaces
-
Resumen
Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of the symmetric geometric rank of a symmetric tensor. This quantity is equal to the codimension of the singular locus of the hypersurface associated to the tensor. We first derive fundamental properties of the symmetric geometric rank. Then, we study the space of symmetric tensors of prescribed symmetric geometric rank, which are spaces of homogeneous polynomials whose corresponding hypersurfaces have a singular locus of bounded codimension.
