Timeline for Restriction of a linear system to a divisor
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 18, 2016 at 14:27 | vote | accept | Li Yutong | ||
| Dec 15, 2016 at 10:39 | comment | added | Sasha | Your $s$ is not a section of a line bundle, it is the ratio of two sections (with the section defining $2D$ in the denominator). It makes no sense to restrict this ratio to $D$. | |
| Dec 15, 2016 at 9:32 | comment | added | Li Yutong | Sorry for keep asking: suppose $L=2D>0$, and $D$ is a fixed component of $|L|$, and then suppose $s\in K(X)$ is a section of $L$, such that $(s) = H - D$ (hence $(s)_0 = H-D + 2D = H+D$). Then how to make sense of $s$ restrict to $D$? I cannot see why it is zero on $D$, actually it has poles on $D$. | |
| Dec 15, 2016 at 9:18 | comment | added | Sasha | If $D$ is a fixed component, then the restriction map is zero. | |
| Dec 15, 2016 at 9:09 | comment | added | Li Yutong | I don't think this is tautology: suppose $D$ is a fixed component of $|L|$, and $s \in K(X)$ is one section whose image is $s_D$, then simply restrict $s$ to $D$ may not be in $K(S)$ (for example, $s$ has poles containing $D$). That is the case I am worry about. | |
| Dec 15, 2016 at 8:11 | history | answered | Sasha | CC BY-SA 3.0 |