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arXiv · 2504.09675

Projective Hypersurfaces of High Degree Admitting an Induced Additive Action

Ivan Beldiev
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Abstract

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 $n-3$.

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Ivan Beldiev. 2025-04-13. Projective Hypersurfaces of High Degree Admitting an Induced Additive Action. https://arxiv.org/abs/2504.09675

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