English

Spherical varieties with the $A_k$-property

Algebraic Geometry 2017-11-13 v4

Abstract

An algebraic variety is said to have the AkA_k-property if any kk points are contained in some common affine open neighbourhood. A theorem of W{\l}odarczyk states that a normal variety has the A2A_2-property if and only if it admits a closed embedding into a toric variety. Spherical varieties can be regarded as a generalization of toric varieties, but they do not have the A2A_2-property in general. We provide a combinatorial criterion for the AkA_k-property of spherical varieties by combining the theory of bunched rings with the Luna-Vust theory of spherical embeddings.

Keywords

Cite

@article{arxiv.1303.5611,
  title  = {Spherical varieties with the $A_k$-property},
  author = {Giuliano Gagliardi},
  journal= {arXiv preprint arXiv:1303.5611},
  year   = {2017}
}

Comments

17 pages

R2 v1 2026-06-21T23:46:36.374Z