论文标题
对称宽矩阵品种的图像闭合
Image closure of symmetric wide-matrix varieties
论文作者
论文摘要
令$ x $为$ k \ times \ times \ mathbb {n} $ - 矩阵和$ y $的仿射方案是$ \ mathbb {n} \ times \ times \ cdots \ times \ times \ times \ times \ mathbb {n} $ - dimensional tensors的仿射方案。组sym $（\ mathbb {n}）$在$ x $和$ y $以及其坐标环上自然作用。我们表明，Zariski闭合Sym $（\ Mathbb {n}）$的图像 - 方案从$ x $到$ y $的等效形态，由有限的许多Sym $（\ Mathbb {n}）$ - $ y $的坐标环中的多个Sym $（\ Mathbb {n}）$。此外，我们证明了这张地图的图像的闭合是sym $（\ mathbb {n}）$ - noetherian，也就是说，sym $（\ mathbb {n}）$的每个下降链稳定稳定。
Let $X$ be an affine scheme of $k \times \mathbb{N}$-matrices and $Y$ be an affine scheme of $\mathbb{N} \times \cdots \times \mathbb{N}$-dimensional tensors. The group Sym$(\mathbb{N})$ acts naturally on both $X$ and $Y$ and on their coordinate rings. We show that the Zariski closure of the image of a Sym$(\mathbb{N})$-equivariant morphism of schemes from $X$ to $Y$ is defined by finitely many Sym$(\mathbb{N})$-orbits in the coordinate ring of $Y$. Moreover, we prove that the closure of the image of this map is Sym$(\mathbb{N})$-Noetherian, that is, every descending chain of Sym$(\mathbb{N})$-stable closed subsets stabilizes.
