发表机构
University of Miami（迈阿密大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该文验证了Winkelmann猜想对正维数仿射半单齐性空间$G/H$成立，证明其驯顺离散集性质及Oka性质，并给出流映射复合的归一化界，特别证明了$\SL_2/N(T)$为RR空间。
AI 中文摘要
Winkelmann猜想每个维数至少为2的光滑柔性复仿射簇都是Rosay-Rudin空间。我们对此在每一个正维数商$G/H$上进行了验证，其中$G$为连通复半单代数群，$H$为连通闭约化子群。弱驯顺与强驯顺一致，驯顺离散集之间的每个单射都延拓为全纯自同构，且驯顺集、有限集或空集的补集都是Oka的。每个足够稀疏的枚举序列都可以通过$n$个完全全纯流映射的复合送到一个固定序列，其中$n\le6$；固定序列的单射自映射允许这样的实现，且$n\le2$。这些流保持一个不变代数体积形式。证明使用整体插值和在两个可解子群下不变的正则函数来构造自同构。若$G$为秩至少为2的单群，且$G/H$为球面齐性空间并容许闭等变嵌入到不可约模中，则归一化界改进为$n\le4$。我们还证明了$\SL_2/N(T)$（其中$T$为极大环面）是RR空间。此商是$\mathbf P^2$中一条光滑二次曲线的补集。
英文摘要
Winkelmann conjectures that every smooth flexible complex affine variety of dimension at least two is a Rosay--Rudin space. We verify this for every positive-dimensional quotient $G/H$ with $G$ a connected complex semisimple algebraic group and $H$ a closed connected reductive subgroup. Weak and strong tameness coincide, every injection between tame discrete sets extends to a holomorphic automorphism, and complements of tame, finite, or empty sets are Oka. Every sufficiently sparse enumerated sequence can be sent to a fixed sequence by a composition of $n$ complete holomorphic flow maps, with $n\le6$; injective self-maps of the fixed sequence admit such a realization with $n\le2$. These flows preserve an invariant algebraic volume form. The proof uses entire interpolation and regular functions invariant under two solvable subgroups to construct the automorphisms. If $G$ is simple of rank at least two and $G/H$ is spherical and admits a closed equivariant embedding into an irreducible module, the normalization bound improves to $n\le4$. We also prove that $\SL_2/N(T)$, where $T$ is a maximal torus, is an RR-space. This quotient is the complement of a smooth conic in $\mathbf P^2$.
Comments30 pages
