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Nov 29, 2009 at 20:24 comment added Charles Siegel Ahh, now I see what you mean.
Nov 29, 2009 at 20:22 comment added Wanderer But it's not affine, and that's really the point of the question!
Nov 29, 2009 at 20:20 comment added Charles Siegel My answer still works. There is no function $f\in k[x,y]$ such that $f=0$ iff $x=y=0$, so $\mathbb{A}^2\setminus\{0\}$ is not determined by the nonvanishing of a single function.
Nov 29, 2009 at 20:18 comment added Wanderer I clarified my question... Sorry for being a bit vague. But your answer doesn't work, obviously.
Nov 29, 2009 at 20:06 history answered Charles Siegel CC BY-SA 2.5