Timeline for inverse image of a pencil of hyperplanes
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2013 at 12:33 | comment | added | Jérémy Blanc | @ leffe: yes, this is exactly this. | |
| Apr 1, 2013 at 12:32 | comment | added | Jérémy Blanc | As a comment, another example in dimension $2$ (which is almost the same as the one of Francesco): let $X\to \mathbb{P}^2$ be the double covering ramified over a smooth quartic. Then, $X$ is a smooth del Pezzo surface of degree $2$ and the pull-back of an hyperplane section is the anticanonical divisor of $X$, which is ample but not very ample (the morphism associated is exactly the double covering). | |
| Apr 1, 2013 at 12:31 | comment | added | leffe | Thanks Francesco! In general the pullback of a very ample divisor will only be ample, so it would be necessary to pass to a power to have something very ample. Does it mean that if I consider a suitable multiple of my embedding $X \hookrightarrow \mathbb{P}^N$ and I replace hyperplane sections by hypersurface sections the condition I want will be verified? | |
| Apr 1, 2013 at 12:12 | history | answered | Francesco Polizzi | CC BY-SA 3.0 |