Timeline for Minimum degree of a variety with $H^i(X,\mathcal{O}_X)\neq 0$ for some $i$ with $0<i<\dim(X)$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 6, 2017 at 19:58 | vote | accept | abx | ||
| Nov 6, 2017 at 16:09 | answer | added | Yusuf Mustopa | timeline score: 12 | |
| Nov 6, 2017 at 14:59 | comment | added | abx | @Yusuf Mustopa: Great, thanks for the reference! Since $X\subset \mathbb{P}^N$ can be projected isomorphically to $\mathbb{P}^{2n+1}$, we get $\deg(X)\geq 2n+4$ unless $X$ is an elliptic scroll, which answers my question. If you want to put this as an answer I'll accept it. | |
| Nov 5, 2017 at 21:00 | comment | added | Yusuf Mustopa | According to a result of Kwak-Park (Theorem A in arxiv.org/pdf/1510.03358.pdf) any bound excluding both elliptic scrolls and varieties with $H^{i}(\mathcal{O})=0$ for $0 < i < n$ has to be at least as sharp as $\deg(X) \geq N+3.$ | |
| Nov 5, 2017 at 0:04 | history | asked | abx | CC BY-SA 3.0 |