Timeline for The kernel of a nef line bundle
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 18, 2017 at 7:42 | comment | added | dorebell | Oops, I missed this - sorry for posting the same answer! They must have gone up around the same time. | |
| Sep 17, 2017 at 4:11 | vote | accept | Vesselin Dimitrov | ||
| Sep 17, 2017 at 4:10 | comment | added | Vesselin Dimitrov | That makes a difference! I had misread the indexing in the definition of $L$, my apology - and thank you for the simple and illuminating example! This question was in too much generality. | |
| Sep 17, 2017 at 4:03 | comment | added | Chiles | The line bundle L is not relatively ample over $\mathbb{P}^1$ but rather over $\mathbb{P}^2$. | |
| Sep 17, 2017 at 3:53 | comment | added | Vesselin Dimitrov | This is a constant family of projective planes, parametrized by the base $B = \mathbb{P}^1$ under $p_1$. In such a case, $\deg_L = 0$ precisely on the constant subvarieties. The section $X \cap Y$ is constant, and has zero intersection with $L$. The line bundle $L$ is relatively ample over $B$, but these intersection numbers take place on the total space $V$, and not in a fibre. In fact $\deg_L(X \cap Y) = 0$ on that example. | |
| Sep 17, 2017 at 3:44 | review | First posts | |||
| Sep 17, 2017 at 6:55 | |||||
| Sep 17, 2017 at 3:41 | history | answered | Chiles | CC BY-SA 3.0 |