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arXiv · 1703.09524

Local and global similarity of holomorphic matrices

Jürgen Leiterer
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Abstract

R. Guralnick (Linear Algebra Appl. 99, 85-96, 1988) proved that two holomorphic matrices on a noncompact connected Riemann surface, which are locally holomorphically similar, are globally holomorphically similar. We generalize this to (possibly, non-smooth) one-dimensional Stein spaces. For Stein spaces of arbitrary dimension, we prove that global $\mathcal C^\infty$ similarity implies global holomorphic similarity, whereas global continuous similarity is not sufficient.

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Jürgen Leiterer. 2017-03-28. Local and global similarity of holomorphic matrices. https://arxiv.org/abs/1703.09524

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