# Equations for GL invariant families of polynomials

@inproceedings{Breiding2021EquationsFG, title={Equations for GL invariant families of polynomials}, author={Paul Breiding and Christian Ikenmeyer and Mateusz Michałek and Reuven Hodges}, year={2021} }

We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer d. It outputs the ideal of that family intersected with the space of homogeneous polynomials of degree d. Our motivation comes from Question 7 in [32] and Problem 13 in [34], which ask to find equations for varieties of cubic and quartic symmetroids. The algorithm relies on a database of specific Young tableaux and…

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