Timeline for Global sections of multiples of a divisor
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 18, 2021 at 20:45 | comment | added | Will Sawin | @GDR It is not true that $h^0(X, mD)$ is necessarily a polynomial function. One can, at least sometimes, prove it is polynomial for $m$ sufficiently large, but this is harder than this argument, and not sufficient anyways. | |
| Jul 18, 2021 at 20:25 | comment | added | Puzzled | Thank you very much to both of you for the answer. Could one argue also by saying that $f(m) = h^0(X,mD)$ is a polynomial function? So if $f(m) = c $ for $m\gg 0$ then $f(m) = c$ for all $m\geq 0$, and hence $f(m) = 1$ for all $m\geq 0$. Is this correct? | |
| Jul 18, 2021 at 19:31 | history | answered | Will Sawin | CC BY-SA 4.0 |