Timeline for Ampleness of the normal bundle to the Albanese image
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 23, 2022 at 17:18 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
deleted 4 characters in body
|
| Sep 23, 2022 at 16:52 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 10 characters in body
|
| Sep 23, 2022 at 5:22 | comment | added | Francesco Polizzi | @abx: ok, thanks. In fact, I only know that the differential of the Albanese map is everywhere of maximal rank. Do you know any example of surface such that $\Omega_X$ is globally generated and $a(X)$ is singular? | |
| Sep 23, 2022 at 4:54 | comment | added | abx | "The Albanese map is a finite, étale cover onto its image": not necessarily. You only know that it is unramified, the image could very well be singular. | |
| Sep 23, 2022 at 0:26 | comment | added | Jason Starr | If $X$ equals a product $C\times D$, then the Albanese morphism for $X$ is the product of the Albanese morphisms of the factors, $\text{alb}_C\times\text{alb}_D:C\times D \to \text{Alb}(C)\times \text{Alb}(D)$. Thus, the pullback of the tangent bundle by the Albanese morphism is the direct sum, $\text{pr}_C^*\text{alb}_C^*T_{\text{Alb}(C)}\oplus \text{pr}_C^*\text{alb}_D^*T_{\text{Alb}(D)}$. Therefore the normal bundle is also a direct sum $\text{pr}_C^* N_{\text{Alb}(C)/C}\oplus \text{pr}_D^*N_{\text{Alb}(D)/D}$. These are not ample on curves in fibers of $\text{pr}_C,\text{pr}_D$. | |
| Sep 22, 2022 at 22:58 | history | edited | LSpice | CC BY-SA 4.0 |
Name of MO187149
|
| Sep 22, 2022 at 22:36 | comment | added | Francesco Polizzi | Thanks for the comment. Could you please give more details? | |
| Sep 22, 2022 at 20:50 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 7 characters in body
|
| Sep 22, 2022 at 10:09 | comment | added | Jason Starr | I think that fails when $X$ is a product of two hyperbolic curves. | |
| Sep 21, 2022 at 16:08 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 17 characters in body
|
| Sep 21, 2022 at 15:54 | history | edited | Francesco Polizzi | CC BY-SA 4.0 |
added 1 character in body; edited title
|
| Sep 21, 2022 at 15:41 | history | asked | Francesco Polizzi | CC BY-SA 4.0 |