Generalized connectedness and Bertini-type theorems over real closed fields
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909887555960832 |
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| author | Ouyang, Yi Zhang, Chenhao |
| author_facet | Ouyang, Yi Zhang, Chenhao |
| contents | In this paper, we establish a real closed analogue of Bertini's theorem. Let $R$ be a real closed field and $X$ a formally real integral algebraic variety over $R$. We show that if the zero locus of a nonzero global section $s$ of an invertible sheaf on $X$ has a formally real generic point, then $s$ does not change sign on $X$, and vice versa under certain conditions. As a consequence, we demonstrate that there exists a nonempty open subset of hypersurface sections preserving formal reality and integrality for quasi-projective varieties of dimension $\geq 2$ under these conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_03277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized connectedness and Bertini-type theorems over real closed fields Ouyang, Yi Zhang, Chenhao Algebraic Geometry 14P25, 12J15 In this paper, we establish a real closed analogue of Bertini's theorem. Let $R$ be a real closed field and $X$ a formally real integral algebraic variety over $R$. We show that if the zero locus of a nonzero global section $s$ of an invertible sheaf on $X$ has a formally real generic point, then $s$ does not change sign on $X$, and vice versa under certain conditions. As a consequence, we demonstrate that there exists a nonempty open subset of hypersurface sections preserving formal reality and integrality for quasi-projective varieties of dimension $\geq 2$ under these conditions. |
| title | Generalized connectedness and Bertini-type theorems over real closed fields |
| topic | Algebraic Geometry 14P25, 12J15 |
| url | https://arxiv.org/abs/2511.03277 |