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arXiv · 2407.06332

On affine Riemann surfaces

Richard Cushman
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Abstract

We show that the universal covering space of a connected component of a regular level set of a smooth complex valued function on ${\mathbb{C}}^2$, which is a smooth affine Riemann surface, is ${\mathbb{R}}^2$. This implies that the orbit space of the action of the covering group on ${\mathbb{R}}^2$ is the original affine Riemann surface.

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Richard Cushman. 2024-07-08. On affine Riemann surfaces. https://arxiv.org/abs/2407.06332

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