Variétés réelles connexes non stablement rationnelles
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912418692595712 |
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| author | Colliot-Thélène, Jean-Louis Pirutka, Alena Scavia, Federico |
| author_facet | Colliot-Thélène, Jean-Louis Pirutka, Alena Scavia, Federico |
| contents | Let $R$ be the field of real Puiseux series. It is a real closed field. We construct the first examples of smooth intersections of two quadrics in $\mathbb{P}_R^5$ and smooth cubic hypersurfaces in $\mathbb{P}_R^4$ which are not stably rational but for which the space $X(R)$ of $R$-points is semi-algebraically connected. The question of constructing such examples over the field of real numbers $\mathbb{R}$ remains open. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21477 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variétés réelles connexes non stablement rationnelles Colliot-Thélène, Jean-Louis Pirutka, Alena Scavia, Federico Algebraic Geometry 14E08 (Primary) 14M20, 14P10, 14P25, 14F20 (Secondary) Let $R$ be the field of real Puiseux series. It is a real closed field. We construct the first examples of smooth intersections of two quadrics in $\mathbb{P}_R^5$ and smooth cubic hypersurfaces in $\mathbb{P}_R^4$ which are not stably rational but for which the space $X(R)$ of $R$-points is semi-algebraically connected. The question of constructing such examples over the field of real numbers $\mathbb{R}$ remains open. |
| title | Variétés réelles connexes non stablement rationnelles |
| topic | Algebraic Geometry 14E08 (Primary) 14M20, 14P10, 14P25, 14F20 (Secondary) |
| url | https://arxiv.org/abs/2505.21477 |