论文标题
无限仿射空间的模棱两可的代数和半代数几何形状
Equivariant algebraic and semi-algebraic geometry of infinite affine space
论文作者
论文摘要
我们研究了$ \ textrm {sym}（\ infty）$ - 不一定在无限的无限多项式环$ \ mathbb {c} [x__ {ij {ij}：\，i \，i \ in \ mathbb {n}，\，\，j，n n [n] $的Zariski频谱中的闭合点。除其他外，我们表征了这枚戒指中不变的理想。此外，我们研究由$ \ textrm {sym}（\ infty）$ orbits在$ \ mathbb {r} [x__ {x__ {ij {ij {ij {ij {ij \，in \ in \ in \ mathbb {n n}，n n}，n n n n n n n n n n}，对于$ n = 1 $，我们证明了量化器消除类型结果，该结果因$ n> 1 $而失败。
We study $\textrm{Sym}(\infty)$-orbit closures of not necessarily closed points in the Zariski spectrum of the infinite polynomial ring $\mathbb{C}[x_{ij}:\, i\in\mathbb{N},\,j\in[n]]$. Among others, we characterize invariant prime ideals in this ring. Furthermore, we study projections of basic equivariant semi-algebraic sets defined by $\textrm{Sym}(\infty)$ orbits of polynomials in $\mathbb{R}[x_{ij}:\, i\in\mathbb{N},\,j\in[n]]$. For $n=1$ we prove a quantifier elimination type result which fails for $n>1$.
