论文标题
多项式函子中的含义性和参数化
Implicitisation and Parameterisation in Polynomial Functors
论文作者
论文摘要
在较早的工作中，第二作者表明，多项式函子的闭合子集始终可以通过有限的多项式方程来定义。在$ \ operatorname {gl} \ nolimits _ {\ infty} $的后续工作中，品种，bik-draisma-eggemont-snowden表明，除其他外，在特征零中，每个这样的封闭式封闭的子集中的特征零，这是一个形态的形象，其域的形象是其域的产物。在本文中，我们表明这两个结果都可以做到算法：存在算法$ \ mathbf {intimisitise} $，将形态作为输入到多项式函数中，并有限地输出许多方程式定义了图像的关闭；和算法$ \ Mathbf {参数} $，它作为输入定义多项式函数的封闭子集的有限方程组，并输出形态，其图像是封闭的子集。
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 $\operatorname{GL}\nolimits_{\infty}$-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 $\mathbf{implicitise}$ that takes as input a morphism into a polynomial functor and outputs finitely many equations defining the closure of the image; and an algorithm $\mathbf{parameterise}$ 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.
