Unipotent Group Actions on Del Pezzo Cones

2012/12/18 by Kishimoto, Takashi, Prokhorov, Yuri, Zaidenberg, Mikhail · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1212.4479

Abstract

In a previous paper we established that for any del Pezzo surface Y of degree at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear system admits an effective Ga-action. In particular, the group Aut(X) is infinite dimensional. In contrast, we show in this note that for a del Pezzo surface Y of degree at most 2 the generalized cones X as above do not admit any non-trivial action of a unipotent algebraic group.

Cited by

• Cylindricity of weighted singular del Pezzo surfaces over fields of characteristic zero
• Cylinders in Du Val del Pezzo surfaces of degree one with Picard rank two

Related

• Group actions on affine cones
• Affine cones over Fano threefolds and additive group actions
• Log del Pezzo surfaces with simple automorphism groups
• Equivariant unirationality of del Pezzo surfaces of degree 3 and 4
• G-coregularity of del Pezzo surfaces