Timeline for Regular Morphism From Affine Line
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2010 at 18:27 | vote | accept | Damien Mondragon | ||
| Oct 10, 2010 at 9:27 | comment | added | Georges Elencwajg | Very nice and geometric. | |
| Oct 10, 2010 at 9:26 | answer | added | Georges Elencwajg | timeline score: 5 | |
| Oct 10, 2010 at 0:27 | comment | added | BCnrd | Yes. Probably there are many solutions. Here is one. We can assume the map is non-constant, so it extends to a non-constant map $f:\mathbf{P}^1 \rightarrow \mathbf{P}^n$ with closed image (due to completeness) that is a curve. As such it meets the hyperplane at infinity, and that intersection must be the point at infinity on $\mathbf{P}^1$ since $f$ carries $\mathbf{A}^1$ into $\mathbf{A}^n$. It follows that the closed set $f(\mathbf{P}^1)$ in $\mathbf{P}^n$ meets $\mathbf{A}^n$ in exactly $f(\mathbf{A}^1)$, so the latter is closed in $\mathbf{A}^n$. | |
| Oct 10, 2010 at 0:11 | history | asked | Damien Mondragon | CC BY-SA 2.5 |