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Timeline for Factorial surfaces and smoothness

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Mar 1 at 14:04 comment added abx No. For instance if $a,b,c$ are three mutually coprime integers, the ring $\mathbb{C}[x,y,z]/(x^{a}+y^{b}+z^{c})$ is factorial (see e.g. Bourbaki, Commutative Algebra VII, §3, exercise 7).
Mar 1 at 12:31 history asked Jooh CC BY-SA 4.0