Timeline for Does there exist an Affinization or Projectivization process for Varieties?
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| May 10, 2016 at 5:19 | comment | added | Isac Hedén | Taking $Y:=\mathrm{Spec}(\mathcal O(X))$ is probably interesting mainly for varieties $X$ that are "alomst" affine, for instance the punctured affine plane (a point is missing), or the blowup of $\mathbb A^2$ at the origin (an affine variety cannot contain $\mathbb P^1$). In both cases $Y$ should be $\mathbb A^2$. The morphism $X\to Y$ should be injective in the first case, and contract $\mathbb P^1$ to a point in the second. If $X=Y\setminus Z$ where Y is affine normal, and $Z$ of codimension at least two, we should have $Y=\mathrm{Spec}(\mathcal O(X))$, i.e. we can recover $Y$ from $X$. | |
| May 9, 2016 at 13:02 | history | answered | Gro-Tsen | CC BY-SA 3.0 |