15 papers
Computing the continuous symmetries of a parametrized variety
Benjamin Biaggi, Jan Draisma, Fulvio Gesmundo +2
We prove that the symmetry Lie algebra of a parametrized variety can be determined directly from the parametrization, without computing the vanishing ideal of the variety. We deriv…
Triangular tensor networks, pencils of matrices and beyond
Alessandra Bernardi, Fulvio Gesmundo
We study tensor network varieties associated with the triangular graph, with a focus on the case where one of the physical dimensions is 2. This allows us to interpret the tensors…
Marvelous slices of orthogonal matrices
Taylor Brysiewicz, Fulvio Gesmundo
The space of special orthogonal matrices with zeros on the diagonal decomposes into the union of irreducible surfaces whose intersections are beautifully encoded…
Polynomials of small slice rank and strength
Cosimo Flavi, Fulvio Gesmundo, Alessandro Oneto +1
This paper investigates defining equations for secant varieties of the variety of reducible polynomials, which geometrically encode the notions of strength and slice rank of homoge…
Linear preservers of secant varieties and other varieties of tensors
Fulvio Gesmundo, Young In Han, Benjamin Lovitz
We study the problem of characterizing linear preserver subgroups of algebraic varieties, with a particular emphasis on secant varieties and other varieties of tensors. We introduc…
Collineation varieties of tensors
Fulvio Gesmundo, Hanieh Keneshlou
In this article, we introduce the -th collineation variety of a third order tensor. This is the closure of the image of the rational map of size minors of a matrix of linear…