Geometry Seminar

Date: May 6, 2024

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: F. Gesmundo, U. Toulouse

Title: Collineation varieties of tensors

Abstract: A linear space of matrices gives rise naturally to a family of algebraic varieties: the k-th collineation variety arises from the parametrization induced by the minors of size k. We propose the study of collineation varieties to obtain `equations' for interesting varieties in the space of tensors. In recent work with Hanieh Keneshlou, we classify these varieties in the case of pencils of matrices and nets of matrices of small dimension. In this seminar, I will introduce this construction and show to what extent the collineation varieties, and their geometric invariants (e.g. their degree), separate orbit-closures and allow us to recover varieties of interest in the study of border rank and border subrank of tensors.