The symmetric geometric rank of symmetric tensors

  • Pierpaola Santarsiero
G3 10 (Lecture hall)


Inspired by recent work of Kopparty-Moshkovitz-Zuiddam and motivated by problems in combinatorics and hypergraphs, we introduce the notion of 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. In this talk, we will first learn fundamental properties of the symmetric geometric rank. Then, we will study the space of symmetric tensors of prescribed symmetric geometric rank, which is the space of homogeneous polynomials whose corresponding hypersurfaces have a singular locus of bounded codimension.

This is joint work with J. Lindberg.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail

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