Timeline for The vanishing of the 2nd plurigenus of a sextic threefold
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 22, 2011 at 4:18 | vote | accept | HNuer | ||
| Feb 21, 2011 at 21:55 | comment | added | diverietti | Of course this is another possibility. The point is that this is a more general property of Fano manifolds... Of course all this needs $X$ to be smooth... | |
| Feb 21, 2011 at 20:36 | comment | added | HNuer | Here's the argument I was thinking of which uses Lefschetz, which I should seen immediately: By Lefschetz $H^{p,q}(\mathbb P^5)$ is isomorphic to $H^{p,q}(C)$ for $p+q<4$, where $C$ is the cubic hypersurface. Applying this again by cutting with the quadric $Q$ to get our $X$, we see that $H^{p,q}(X)$ is isomorphic to $H^{p,q}(C)$ for $p+q<3$. Since the $h^{p,q}(\mathbb P^n)=0$ for $p\neq q$, this gives our result. I suppose since one proves Lefschetz with Kodaira vanishing, it's all the same really, but this is what I had in mind originally. | |
| Feb 21, 2011 at 18:30 | answer | added | diverietti | timeline score: 5 | |
| Feb 21, 2011 at 18:09 | answer | added | Johannes Nordström | timeline score: 8 | |
| Feb 21, 2011 at 16:30 | history | asked | HNuer | CC BY-SA 2.5 |