一维 Stein 空间上全纯矩阵的相似性
复变函数
2018-02-06 v4
摘要
R. Guralnick [Linear Algebra Appl. 99, 85-96 (1988)] 证明了：在非紧连通 Riemann 曲面上两个局部全纯相似的全纯矩阵是全局全纯相似的。在预印本 [arXiv:1703.09524] 与 [arXiv:1703.09530] 中，已将这一结论推广到任意（可能非光滑的）一维 Stein 空间。本文包含 [arXiv:1703.09524] 中证明的修订版本。这一修订证明的方法亦可应用于高维情形，这将成为后续论文的主题。
引用
@article{arxiv.1710.10969,
title = {Similarity of holomorphic matrices on 1-dimensional Stein spaces},
author = {Jürgen Leiterer},
journal= {arXiv preprint arXiv:1710.10969},
year = {2018}
}
备注
This is a revised version of a part of a preprint from Sep 2016, later (Mar 2017) posted as arXiv:1703.09524. Version 2 is a mistake (the wrong file was sent). The differences of version 3 to version 1 are: a "Note added in proof" and a reference are added, typos are corrected. The difference of version 4 to version 3 is: some small corrections are carried out, rusults unchanged