Cœuré-Loeb 例子作为 Stein 空间的开子集
The Cœuré-Loeb example as an open subset of a Stein space
中文总结 AI 辅助
本文针对塞尔问题，证明了 Cœuré-Loeb 纤维化可作为 Stein 空间的开子集（即 Stein 空间中某解析集的补集），补充了该问题反例的结构性质。
中文摘要 AI 辅助
塞尔问题询问：具有 Stein 基和 Stein 纤维的局部平凡全纯纤维化本身是否为 Stein。Skoda 构造了该问题的首个反例。后来 Cœuré 和 Loeb 构造了另一显著反例，其纤维为有界全纯域。该纤维化的全空间具有可分点并提供局部坐标的全局全纯函数，但它不允许 Stein 全纯包络。本文证明，Cœuré-Loeb 纤维化可实现为 Stein 空间的开子集，更准确地说，它是 Stein 空间中某解析集的补集。
英文摘要
The Serre problem asked if a locally trivial holomorphic fibration with Stein base and Stein fiber is itself Stein. \v Skoda constructed the first counterexample for this problem. Later, Cœuré and Loeb constructed another remarkable counterexample, with bounded domain of holomorphy as fiber. The total space of their fibration has global holomorphic functions which separate points and provide local coordinates. However, it does not admit a Stein envelope of holomorphy. In this paper, we prove that the Cœuré--Loeb fibration can be realized as an open subset of a Stein space, more precisely it is the complement of an analytic set in a Stein space.
