English

Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups

Algebraic Geometry 2026-03-24 v2

Abstract

Given a connected reductive algebraic group GG with a Borel subgroup BB and a quasiaffine spherical GG-variety XX, we prove that every GG-orbit YY contained in the regular locus of XX can be connected by a BB-normalized additive one-parameter group action with any minimal GG-orbit in XX containing YY in its closure. As a consequence, we show that the regular locus of XX is transitive for the subgroup in the automorphism group of XX generated by GG and all BB-normalized additive one-parameter subgroups.

Keywords

Cite

@article{arxiv.2512.09906,
  title  = {Connecting orbits in quasiaffine spherical varieties via $B$-root subgroups},
  author = {Roman Avdeev and Vladimir Zhgoon},
  journal= {arXiv preprint arXiv:2512.09906},
  year   = {2026}
}

Comments

v2: 9 pages; the main part is rewritten

R2 v1 2026-07-01T08:19:15.977Z