English

Equivariant compactifications of two-dimensional algebraic groups

Algebraic Geometry 2013-05-13 v2 Number Theory

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.

Keywords

Cite

@article{arxiv.1212.3518,
  title  = {Equivariant compactifications of two-dimensional algebraic groups},
  author = {Ulrich Derenthal and Daniel Loughran},
  journal= {arXiv preprint arXiv:1212.3518},
  year   = {2013}
}

Comments

19 pages, 1 figure

R2 v1 2026-06-21T22:54:37.967Z