Obstructions to tensor degeneration via multilinear Fano schemes

To characterize tensors, determining obstructions to tensor restriction and degeneration is a fundamental problem. In this talk, I will introduce a geometric invariant of tensors, called the multilinear Fano scheme, and we use it to provide some obstructions to degenerations of tensors. The multilinear Fano scheme is an algebraic scheme in a product of Grassmannians, parametrizing products of spaces on which a tensor vanishes. It generalizes several other constructions, such as the geometric rank, the slice rank, the notion of compressibility, and the classical Fano scheme of a hypersurface. I will state some results we have regarding the multilinear Fano scheme and its dimension.
This is a joint work with Fulvio Gesmundo and Jeroen Zuiddam. 

This seminar is part of the Problems in Algebraic Geometry Coming from Complexity Theory series.