Timeline for Castelnuovo's rationality criterion on singular surfaces?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 13, 2014 at 17:33 | vote | accept | Jesus Martinez Garcia | ||
| Jun 13, 2014 at 17:33 | comment | added | Jesus Martinez Garcia | Ooops, the du Val case is so obvious, you are right. Glad to see that it is sharp for singularities. Thanks. | |
| Jun 10, 2014 at 6:26 | comment | added | abx | The OP gave the definitions he is using, namely $q(S)=h^1(\mathcal O_S)$ and $P_2(S)=h^0(\mathcal O_S(2K_S))$. This is what I use in the examples. | |
| Jun 9, 2014 at 23:18 | comment | added | Felipe Voloch | If $q$ were to be defined as the dimension of the Albanese of $S$ (for a reasonable definition of Albanese in the singular case), then this example would not work, as the Albanese should be the cubic. What happens with this definition? I suppose if one uses birational invariants, then it doesn't matter if the surface is smooth or not. | |
| Jun 9, 2014 at 20:56 | history | answered | abx | CC BY-SA 3.0 |