On G-birational rigidity of projective spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915949063438336 |
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| author | Cheltsov, Ivan Mangolte, Frederic Shramov, Constantin |
| author_facet | Cheltsov, Ivan Mangolte, Frederic Shramov, Constantin |
| contents | In this paper, we study finite subgroups $G\subset\mathrm{Aut}(\mathbb{P}^n)$ such that $\mathbb{P}^n$ is $G$-birationally rigid. For each $n\geqslant 3$, we prove that $\mathrm{Aut}(\mathbb{P}^n)$ contains at most finitely many such subgroups up to conjugation. For $n=4$, we prove that $\mathbb{P}^4$ is $G$-birationally superrigid if $G\simeq\mathrm{PSp}_{4}(\mathbf{F}_3)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20427 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On G-birational rigidity of projective spaces Cheltsov, Ivan Mangolte, Frederic Shramov, Constantin Algebraic Geometry In this paper, we study finite subgroups $G\subset\mathrm{Aut}(\mathbb{P}^n)$ such that $\mathbb{P}^n$ is $G$-birationally rigid. For each $n\geqslant 3$, we prove that $\mathrm{Aut}(\mathbb{P}^n)$ contains at most finitely many such subgroups up to conjugation. For $n=4$, we prove that $\mathbb{P}^4$ is $G$-birationally superrigid if $G\simeq\mathrm{PSp}_{4}(\mathbf{F}_3)$. |
| title | On G-birational rigidity of projective spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2604.20427 |