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arXiv · 1405.5391

A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki

Karol Palka
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Abstract

Using the theory of minimal models of quasi-projective surfaces we give a new proof of the theorem of Lin-Zaidenberg which says that every topologically contractible algebraic curve in the complex affine plane has equation $X^n=Y^m$ in some algebraic coordinates on the plane. This gives also a proof of the theorem of Abhyankar-Moh-Suzuki concerning embeddings of the complex line into the plane. Independently, we show how to deduce the latter theorem from basic properties of $\mathbb{Q}$-acyclic surfaces.

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Karol Palka. 2014-05-21. A new proof of the theorems of Lin-Zaidenberg and Abhyankar-Moh-Suzuki. https://doi.org/10.1142/s0219498815400125

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