Timeline for Why only some del Pezzo are toric?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6, 2019 at 13:54 | comment | added | Jérémy Blanc | Thanks for the answer. | |
| Apr 5, 2019 at 6:35 | comment | added | Pop | To answer your second question: If I counted parameters correctly, given 10 points in the plane there is a curve of degree 9 with multiplicity 3 at 8 of the points and multiplicity 2 at the other 2. Its intersection with the anticanonical is $3 \cdot 9 - 8 \cdot 3 - 2 \cdot 2 =-1$. | |
| Apr 4, 2019 at 21:18 | comment | added | Pop | Dear J\'er\'emy, a nef divisor on a surface always has nonnegative selfintersection. For 9+n points the anticanonical has selfintersection -n, so it cannot be nef. | |
| Apr 4, 2019 at 12:42 | comment | added | Jérémy Blanc | For $9$, it is certainly nef, but for $10$, why should it be not nef? Which curve is positive against the canonical divisor? | |
| Apr 1, 2019 at 13:53 | comment | added | Pop | Small clarification to the last line: if you blow up more than 9 points, the anticanonical is not even nef. | |
| Apr 1, 2019 at 13:37 | history | answered | Jérémy Blanc | CC BY-SA 4.0 |