Equivariant algebraic and semi-algebraic geometry of infinite affine space
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866911404625231872 |
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| author | Kummer, Mario Riener, Cordian |
| author_facet | Kummer, Mario Riener, Cordian |
| contents | 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 $n>1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_11921 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Equivariant algebraic and semi-algebraic geometry of infinite affine space Kummer, Mario Riener, Cordian Algebraic Geometry 13E05, 14P10 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 $n>1$. |
| title | Equivariant algebraic and semi-algebraic geometry of infinite affine space |
| topic | Algebraic Geometry 13E05, 14P10 |
| url | https://arxiv.org/abs/2203.11921 |