Timeline for Smoothness of Symmetric Powers
Current License: CC BY-SA 2.5
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Jan 2, 2010 at 1:03 | comment | added | Jorge Vitório Pereira | I was thinking on curves over $\mathbb R$, or more precisely on its real points. According to VA's answer the symmetric powers of $\mathbb A^1$ are smooth while the symmetric powers of $\mathbb A^1(\mathbb R)=\mathbb R$, as real manifolds, are not. For $\mathbb A^2$ and $\mathbb A^2(\mathbb R) = \mathbb R^2$ we have the reverse phenomenon. | |
| Jan 1, 2010 at 21:44 | history | edited | Jorge Vitório Pereira | CC BY-SA 2.5 |
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| Jan 1, 2010 at 15:43 | history | edited | Jorge Vitório Pereira | CC BY-SA 2.5 |
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| Jan 1, 2010 at 14:59 | comment | added | David E Speyer | I disagree. These examples show that "curve" and "surface" mean something different in algebraic and differential geometry, because algebraic geometers usually describe things by their complex dimension. What you are calling surfaces are being called curves in the other answers. But we agree about which objects are smooth. | |
| Jan 1, 2010 at 14:47 | history | answered | Jorge Vitório Pereira | CC BY-SA 2.5 |