Timeline for Unirational implies rationally connected
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2013 at 17:04 | comment | added | Puzzled | If X is projective and two general points can be connected by a rational curve then any two points can be connected by a rational curve. | |
| Oct 16, 2013 at 21:10 | comment | added | HNuer | I acknowledged, after Jack's comments above, that your proof works for the usual definition of rationally connected, namely that two general points can be connected by a rational curve. However, I edited the question to more clearly reflect what I was asking which was why ANY two points can be connected by a chain of rational curves. | |
| Oct 16, 2013 at 17:03 | comment | added | Puzzled | Yes, $\phi_{|L}$ is a morphism just because $L$ is a smooth curve. I am assuming $X$ projective. | |
| Oct 16, 2013 at 16:54 | comment | added | Sándor Kovács | @Scott: $L$ is a smooth projective curve. There is no room for indeterminacy. (I suppose one may assume that $X$ is projective as well). | |
| Oct 16, 2013 at 15:46 | comment | added | S. Carnahan♦ | Why is $\phi|_L$ a morphism instead of a rational map? | |
| Oct 16, 2013 at 13:40 | history | answered | Puzzled | CC BY-SA 3.0 |