On a result of Miyanishi-Masuda

Details On a result of Miyanishi-Masuda On a result of Miyanishi-Masuda

2005-06-13

arxiv.org/abs/math/0506235v1

Mathematics

Algebraic Geometry

3 pages

Scientific paper

Let $X$ be an affine surface admitting a unique affine ruling and a $\mathbb
C^*$-action. Assume that the ruling has a unique degenerate fibre and that this
fibre is irreducible. In this paper we give a short proof of the following
result of Miyanishi and Masuda: the universal covering of $X$ is a hypersurface
in the affine 3-space given by the equation $x^my=z^d-1$, where $m>1$.

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