On Normality of Projective Hypersurfaces with an Additive Action

2024/04/29 by Ivan Arzhantsev, Arzhantsev, Ivan, Ivan Beldiev +3 · 2 citations
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Theoretical and Applied Studies in Material Sciences and Geometry #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2404.18484

openalex publication_date 2024/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study projective hypersurfaces X admitting an induced additive action, i.e., an effective action \mathbb G_a^m× X→ 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.

Cited by

• Induced additive actions on toric varieties
• Limit points of one-parameter subgroups for additive actions on hypersurfaces

Related

• Projective Hypersurfaces of High Degree Admitting an Induced Additive Action
• Additive actions on projective hypersurfaces with a finite number of orbits
• Gorenstein Algebras and Uniqueness of Additive Actions
• Additive actions on toric projective hypersurfaces
• Induced additive actions on toric varieties