发表机构
HSE University; Lomonosov Moscow State University（高等经济学院; 莫斯科罗蒙诺索夫国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究环面球簇自同构群的轨道，在仿射情形和光滑完备情形下分别给出了两点同轨道的判别准则，用$B$-稳定素除子及其类生成的幺半群描述核。
AI 中文摘要
本文研究了环面球簇上自同构群的轨道。在仿射情形下，我们证明了两个点属于单位分支的同一轨道当且仅当从除子类群到其局部除子类群的同态核一致。这些核用$B$-稳定素除子来描述。对于光滑完备的环面球簇，我们利用由不包含给定$G$-轨道的$B$-稳定素除子类生成的幺半群，得到了类似的判别准则。
英文摘要
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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