PreprintCC BY 4.0arXiv
On orbits of the automorphism group of toroidal spherical varieties
Abstract
In this paper we study the orbits of the automorphism group on a toroidal spherical variety. In the affine case, we prove that two points lie in the same orbit of the identity component if and only if the kernels of the homomorphisms from the divisor class group to their local divisor class groups coincide. These kernels are described in terms of B-stable prime divisors. For a smooth complete toroidal spherical variety, we obtain a similar criterion using the monoids generated by the classes of B-stable prime divisors that do not contain a given G-orbit.
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BibTeX
@misc{chernov2026orbits,
title = {{On orbits of the automorphism group of toroidal spherical varieties}},
author = {Alexander Chernov and Klim Rolgin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.35683},
eprint = {2609.35683},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35683},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On orbits of the automorphism group of toroidal spherical varieties
AU - Alexander Chernov
AU - Klim Rolgin
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2609.35683
UR - https://arxiv.org/abs/2609.35683
AB - In this paper we study the orbits of the automorphism group on a toroidal spherical variety. In the affine case, we prove that two points lie in the same orbit of the identity component if and only if the kernels of the homomorphisms from the divisor class group to their local divisor class groups coincide. These kernels are described in terms of B-stable prime divisors. For a smooth complete toroidal spherical variety, we obtain a similar criterion using the monoids generated by the classes of B-stable prime divisors that do not contain a given G-orbit.
ER -