Equivariant compactifications of two-dimensional algebraic groups

2012/12/14 by Derenthal, Ulrich, Loughran, Daniel · 1 citation
#11D45 (Secondary) #14L30 (Primary) 14J26 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1212.3518

Abstract

We classify generically transitive actions of semidirect products of an additive and a multiplicative group on the projective plane. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's conjecture), we determine all (possibly singular) del Pezzo surfaces that are equivariant compactifications of homogeneous spaces for such semidirect products.

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• Induced additive actions on toric varieties

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