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Why are $\mathbb A_k^2 \backslash \{(0,0) \} $ and $\mathbb P_k^2 \backslash \{(0,0) \} $ isomorphic to neither affine nor projective varieties?

I've seen this question in several different places, but haven't been able to do it. Any hints/explanations appreciated. Thanks

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    Relevant: (http://math.stackexchange.com/questions/101262/projective-varieties-basics) and (http://math.stackexchange.com/questions/122821/mathbba2-not-isomorphic-to-affine-space-minus-the-origin/122826#122826)2012-04-26

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