Timeline for Torsion line bundles with non-vanishing cohomology on smooth ACM surfaces
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 19, 2010 at 2:47 | vote | accept | Hailong Dao | ||
| Dec 9, 2009 at 18:06 | comment | added | Hailong Dao | Dear Dmitri, I did mean all $k$(here I fixed a very ample line bundle $mathcal O_X(1)$). This is quite restrictive, I am aware of that. | |
| Dec 9, 2009 at 17:00 | comment | added | Dmitri Panov | Dear Hailong, it will be very helpfull if you specify what you mean by $H^1(\mathcal O(k))=0$. For example is $k$ an integer number? In this case, can it be $0$? If it $k=0$, does this mean for you that $O(0)$ is just the structure sheaf of $X$? In this case it follows that your surface has $H^1(X)=0$. Also do I understand correctly that for you $mathcal O(1))$ is ANY ample line bundle? | |
| Dec 9, 2009 at 15:58 | comment | added | Hailong Dao | Thanks! What about without the global generation condition? I realized I did not need it that much. | |
| Dec 9, 2009 at 14:51 | history | answered | Dmitri Panov | CC BY-SA 2.5 |