Limit points of one-parameter subgroups for additive actions on hypersurfaces

2025/05/06 by Anton Shafarevich, Shafarevich, Anton
Mathematics · #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2505.03924

openalex publication_date 2025/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By an additive action on an algebraic variety X over ℂ, we mean an action of the group \mathbbG_aⁿ = ℂⁿ on X with an open orbit. We study limit points of one-dimensional subgroups of \mathbbG_aⁿ for additive actions on projective hypersurfaces. We say that an additive action on X satisfies the OP-condition if for every point x∈ X that does not lie in the open orbit O there is a point y ∈ O and a vector v ∈ \mathbbG_aⁿ such that lim_t→∞ tv∘ y = x. We find all projective hypersurfaces on which there is an additive action satisfying the OP-condition.

Citations

• Toric varieties admitting an action of a unipotent group with a finite number of orbits
• Additive actions on projective hypersurfaces with a finite number of orbits
• On Normality of Projective Hypersurfaces with an Additive Action
• Gorenstein Algebras and Uniqueness of Additive Actions
• Hyperplane Arrangements and Compactifications of Vector Groups
• Enumeration of points, lines, planes, etc
• The closure of a linear space in a product of lines
• The closure of a linear space in a product of lines
• Hassett-Tschinkel correspondence and automorphisms of the quadric
• Geometry of equivariant compactifications of Gⁿ_a

Related

• Additive actions on projective hypersurfaces with a finite number of orbits
• Projective Hypersurfaces of High Degree Admitting an Induced Additive Action
• Additive actions on toric projective hypersurfaces
• Additive actions on projective surfaces with a finite number of orbits
• Additive actions on complete toric surfaces