Projective Hypersurfaces of High Degree Admitting an Induced Additive Action
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909578797514752 |
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| author | Beldiev, Ivan |
| author_facet | Beldiev, Ivan |
| contents | We study induced additive actions on projective hypersurfaces, i.e. effective regular actions of the algebraic group $\mathbb G_a^m$ with an open orbit that can be extended to a regular action on the ambient projective space. It is known that the degree of a hypersurface $X\subseteq\mathbb{P}^n$ admitting an induced additive action cannot be greater than $n$ and there is a unique such hypersurface of degree $n$. We give a complete classification of hypersurfaces $X\subseteq \mathbb{P}^n$ admitting an induced additive action of degrees from $n-1$ to $n-3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09675 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Projective Hypersurfaces of High Degree Admitting an Induced Additive Action Beldiev, Ivan Algebraic Geometry We study induced additive actions on projective hypersurfaces, i.e. effective regular actions of the algebraic group $\mathbb G_a^m$ with an open orbit that can be extended to a regular action on the ambient projective space. It is known that the degree of a hypersurface $X\subseteq\mathbb{P}^n$ admitting an induced additive action cannot be greater than $n$ and there is a unique such hypersurface of degree $n$. We give a complete classification of hypersurfaces $X\subseteq \mathbb{P}^n$ admitting an induced additive action of degrees from $n-1$ to $n-3$. |
| title | Projective Hypersurfaces of High Degree Admitting an Induced Additive Action |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.09675 |