Gorenstein Algebras and Uniqueness of Additive Actions

2023/03/09 by Ivan Beldiev, Beldiev, Ivan · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2303.05573

openalex publication_date 2023/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study induced additive actions on projective hypersurfaces, i.e. 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. We prove that if a projective hypersurface admits an induced additive action, then it is unique if and only if the hypersurface is non-degenerate. We also show that for any n≥ 2, there exists a non-degenerate hypersurface in \mathbb Pⁿ of each degree d from 2 to n.

Cited by

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

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