Additive actions on projective surfaces with a finite number of orbits
Algebraic Geometry
2025-08-12 v1
Abstract
An additive action on an algebraic variety is an effective action of the vector group with an open orbit. We describe projective surfaces with du Val singularities that admit an additive action with a finite number of orbits. In particular, we provide examples of projective surfaces with 1-parameter families of pairwise non-isomorphic additive actions, which answers the question by Hassett and Tschinkel.
Cite
@article{arxiv.2508.07924,
title = {Additive actions on projective surfaces with a finite number of orbits},
author = {Alexander Perepechko},
journal= {arXiv preprint arXiv:2508.07924},
year = {2025}
}
Comments
13 pages, 1 figure, 1 table