Del Pezzo quintics as equivariant compactifications of vector groups

2022/09/09 by Adrien Dubouloz, Takashi Kishimoto, Dubouloz, Adrien +3
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2209.04152

openalex publication_date 2022/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study faithful actions with a dense orbit of abelian unipotent groups on quintic del Pezzo varieties over a field of characteristic zero. Such varieties are forms of linear sections of the Grassmannian of planes in a 5-dimensional vector space. We characterize which smooth forms admit these types of actions and show that in case of existence, the action is unique up to equivalence by automorphisms. We also give a similar classification for mildly singular quintic del Pezzo threefolds and surfaces.

Related

• Equivariant compactifications of two-dimensional algebraic groups
• Quintic del Pezzo threefolds in positive and mixed characteristic
• Automorphisms of quartic del Pezzo surfaces in characteristic zero
• Singular del Pezzo surfaces that are equivariant compactifications
• Log del Pezzo surfaces with simple automorphism groups