Implicitisation and Parameterisation in Polynomial Functors
Publisher DOI
Abstract
In earlier work, the second author showed that a closed subset of a polynomial functor can always be defined by finitely many polynomial equations. In follow-up work on GL_{\infty}-varieties, Bik–Draisma–Eggermont–Snowden showed, among other things, that in characteristic zero every such closed subset is the image of a morphism whose domain is the product of a finite-dimensional affine variety and a polynomial functor. In this paper, we show that both results can be made algorithmic: there exists an algorithm that takes as input a morphism into a polynomial functor and outputs finitely many equations defining the closure of the image; and an algorithm that takes as input a finite set of equations defining a closed subset of a polynomial functor and outputs a morphism whose image is that closed subset.
Date Issued
2023
Publication Type
Article
Subject(s)
Language(s)
en
Additional Credits
Journal
Foundations of computational mathematics
Publisher
Springer
ISSN
1615-3375
Access(Rights)
open.access