On Normality of Projective Hypersurfaces with an Additive Action
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917046430728192 |
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| author | Arzhantsev, Ivan Beldiev, Ivan Zaitseva, Yulia |
| author_facet | Arzhantsev, Ivan Beldiev, Ivan Zaitseva, Yulia |
| contents | We study projective hypersurfaces $X$ admitting an induced additive action, i.e., an effective action ${\mathbb G_a^m\times X\to X}$ of the vector group $\mathbb G_a^m$ with an open orbit that can be extended to an action on the ambient projective space. A criterion for normality of such a hypersurface $X$ is given. Also, we prove that for any projective hypersurface $Z$ there exists a hypersurface $X$ with an induced additive action such that the complement to the open $\mathbb G_a^m$-orbit in $X$ is a projective cone over $Z$. We introduce a construction that produces non-degenerate hypersurfaces with induced additive action from Young diagrams and study the properties of the hypersurfaces obtained in this way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18484 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Normality of Projective Hypersurfaces with an Additive Action Arzhantsev, Ivan Beldiev, Ivan Zaitseva, Yulia Algebraic Geometry We study projective hypersurfaces $X$ admitting an induced additive action, i.e., an effective action ${\mathbb G_a^m\times X\to X}$ of the vector group $\mathbb G_a^m$ with an open orbit that can be extended to an action on the ambient projective space. A criterion for normality of such a hypersurface $X$ is given. Also, we prove that for any projective hypersurface $Z$ there exists a hypersurface $X$ with an induced additive action such that the complement to the open $\mathbb G_a^m$-orbit in $X$ is a projective cone over $Z$. We introduce a construction that produces non-degenerate hypersurfaces with induced additive action from Young diagrams and study the properties of the hypersurfaces obtained in this way. |
| title | On Normality of Projective Hypersurfaces with an Additive Action |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2404.18484 |