Timeline for Inclusion of logarithmic de-Rham complex into differentials
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 25, 2018 at 0:46 | comment | added | lemiller | Sorry to be late to the party, but do the answers change if one replaces X by a smooth rigid analytic space? | |
| Sep 27, 2012 at 3:13 | answer | added | Sándor Kovács | timeline score: 4 | |
| Sep 27, 2012 at 2:07 | comment | added | LMN | Great, thanks! If you reply below, I'll be happy to accept your response as an answer. | |
| Sep 27, 2012 at 1:41 | history | edited | LMN |
edited tags
|
|
| Sep 27, 2012 at 1:40 | comment | added | Pavel Safronov | Sorry, I didn't understand your question at first. Forms in $j_*\Omega^k_U$ are definitely not $C^\infty$ on $X$, since they are not even defined at $D$. Let me try to be more precise. The kernel of $\Omega^k_X(*D)\rightarrow j_*\Omega^k_U$ consists of meromorphic forms on $X$ which vanish on $U$. Since they are zero on an open set, they are zero on the whole $X$. | |
| Sep 27, 2012 at 1:17 | comment | added | LMN | Why do you know that $j_*\Omega_U^k$ is the sheaf of $C^\infty$ differential $k$-forms on $X$ that are holomorphic on $U$? | |
| Sep 27, 2012 at 1:11 | comment | added | Pavel Safronov | $j_*\Omega^k_U$ is the sheaf of differential forms which are holomorphic on $U$. You have an inclusion $\Omega^k_X(*D)\subset j_*\Omega^k_U$ of forms meromorphic along $D$. Furthermore, $\Omega^k_X(log D)\subset \Omega^k_X(*D)$ as forms having a first-order pole along $D$. | |
| Sep 27, 2012 at 0:59 | history | asked | LMN | CC BY-SA 3.0 |