Timeline for bound on the genus of a fiber of the Albanese map of a surface with $h^1({\mathcal O})=1$?
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 29, 2011 at 18:26 | comment | added | rita | If $K_S-F$ is effective, than of course I have a bound since $K_S(K_S-F)\ge 0$ and $K_SF=2g(F)-2$. And by the same argument, I would have a bound if I could determine explicitly an $m$ such that $mK_S-F$ is effective, but that's precisely what I don't know how to do. | |
| Mar 28, 2011 at 4:42 | comment | added | Tong | I GUESS in some sense you can make it. For example, you can consider the canonical map of the surface, which will work if $K_S^2$ is not so small. Assume that the fiber of the Albanese map is $F$, then consider whether $\mathscr{O}(K_S-F)$ has global section or not. If it has a global section, then after computing some intersection number, maybe you can have a bound of $g(F)$. | |
| Dec 12, 2010 at 20:46 | history | edited | rita | CC BY-SA 2.5 |
added 9 characters in body; edited body
|
| Dec 12, 2010 at 20:30 | history | edited | rita | CC BY-SA 2.5 |
added 31 characters in body
|
| Dec 12, 2010 at 20:12 | history | asked | rita | CC BY-SA 2.5 |