Timeline for nonvanishing higher cohomology of a very ample divisor
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 19, 2020 at 20:21 | comment | added | Jason Starr | You are welcome. | |
| Oct 19, 2020 at 11:12 | comment | added | Evgeny Shinder | Thanks, Jason, that's great! I see that the projection of $X$ to the the first factor $\mathbf{P}^2$ identifies $X$ with a blow up of $\mathbf{P}^2$ in $d^2$ points obtained from a pair of intersecting degree $d$ plane curves, in particular $X$ is rational and so $p_g(X) = q(X) = 0$. Furthermore, I see how for large $d$, $\chi(L) < 0$, hence $L$ has nonvanishing $h^1$. | |
| Oct 19, 2020 at 0:51 | comment | added | Jason Starr | Take a hypersurface in $\mathbb{P}^2\times\mathbb{P}^1$ of bidegree $(d,1)$ for $d>3$ with the very ample invertible sheaf of bidegree $(1,1)$. | |
| Oct 18, 2020 at 22:26 | history | asked | Evgeny Shinder | CC BY-SA 4.0 |