Timeline for Canonical bundle of a general surface section
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 15, 2023 at 18:01 | comment | added | abx | (1) follows from $\mathscr{N}_{S/X}^*\cong \mathscr{I}/\mathscr{I}^2$, where $\mathscr{I}$ is the ideal sheaf of $S$ in $X$. Yes, your argument for (2) is correct. | |
| Nov 15, 2023 at 14:20 | comment | added | Proj | @abx, Could you please briefly indicate if $(1)$ follows directly by definition or some exact sequence involving normal bundle, if the argument given for $(2)$ is correct? | |
| Nov 14, 2023 at 14:43 | review | Close votes | |||
| Dec 1, 2023 at 3:08 | |||||
| Nov 14, 2023 at 14:18 | comment | added | abx | (1) Yes. The normal bundle is $H^{{\scriptscriptstyle\oplus }(n-2)}.\hskip3.5cm$ (2) Yes, $K_S$ is nef; no, it is not necessarily effective.$\hskip1.3cm$ (3) $K_S$ is nef if and only if $S$ is minimal of Kodaira dimension $\geq 0.\hskip9cm$ This being said, your questions would be more appropriate at MSE. | |
| S Nov 14, 2023 at 11:35 | review | First questions | |||
| Nov 14, 2023 at 14:21 | |||||
| S Nov 14, 2023 at 11:35 | history | asked | Proj | CC BY-SA 4.0 |