Timeline for Negative self-intersection and finiteness
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2015 at 17:43 | comment | added | Remke Kloosterman | There are many type of sections. First the 9 exceptional divisors are sections. Then the lines through 2 of the 9 base points are sections, conics through 5 of the 9 base points are sections, cubics through 7 of the 9 base points, which have a node at one of the 7 points are also sections, etc. | |
| Sep 23, 2015 at 14:05 | comment | added | user39380 | If we project a section to $\mathbb{P}^2$, we will get a line, but any line would meet a cubic in $3$ points, but the section should meet a fiber in one point, I wasn't quite understanding this.. | |
| Sep 23, 2015 at 13:25 | comment | added | Remke Kloosterman | The Picard group of $S$ has rank 10, hence there are at most 9 disjoint -1 curves. If $C_1$ and $C_2$ intersect in 9 distinct points then there are 9 disjoint -1 curves. For rational elliptic surfaces the group of sections is finitely generated. | |
| Sep 23, 2015 at 13:05 | vote | accept | CommunityBot | ||
| Sep 23, 2015 at 13:05 | comment | added | user39380 | Is the abelian group of sections finitely generated? How many disjoint sections it has at most？ | |
| Sep 23, 2015 at 13:00 | vote | accept | CommunityBot | ||
| Sep 23, 2015 at 13:05 | |||||
| Sep 23, 2015 at 12:07 | history | answered | Remke Kloosterman | CC BY-SA 3.0 |