A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866908539002290176 |
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| author | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| author_facet | Gori, Anna Sarfatti, Giulia Vlacci, Fabio |
| contents | In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common zeros of slice regular polynomials which belong to an ideal in $\mathbb H[q_1,\ldots,q_n]$. This study motivates the introduction of a new notion of algebraic set in the quaternionic setting, which allows us to define a Zariski-type topology on $\mathbb H^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables Gori, Anna Sarfatti, Giulia Vlacci, Fabio Complex Variables Algebraic Geometry 30G35, 16S36, 15A54 In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common zeros of slice regular polynomials which belong to an ideal in $\mathbb H[q_1,\ldots,q_n]$. This study motivates the introduction of a new notion of algebraic set in the quaternionic setting, which allows us to define a Zariski-type topology on $\mathbb H^n$. |
| title | A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables |
| topic | Complex Variables Algebraic Geometry 30G35, 16S36, 15A54 |
| url | https://arxiv.org/abs/2402.16784 |