Timeline for A problem related to deformation of irrational curves
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2014 at 1:55 | comment | added | Li Yutong | @user76758 I see what you mean. However, where I got wrong in the statement? I checked two books on MMP (Debarre and Matsuki), book proves seems rely on that claim | |
| Jun 1, 2014 at 1:50 | comment | added | user76758 | @LiYutong: In the case of interest one can see that the degree of the $f_t$'s is bounded, so that can avoid your proposed counterexamples (if we allow ourselves to drop some $t$'s). But degree bound alone is insufficient, as my previous comment indicates. | |
| Jun 1, 2014 at 1:49 | comment | added | user76758 | It isn't true that any two pointed finite maps from $C$ onto a fixed target curve are related through an automorphism of the source: at the very least one needs to bring in degree bounds (which certainly hold in the case of interest) but one also has to rule out other things such as automorphisms of the target which preserve the base point (of which there can be infinitely many when the target curve is a rational curve). | |
| Jun 1, 2014 at 1:47 | comment | added | Li Yutong | I don't understand your claim that "$f_{t'},f_{t}$ differ by an autumorphism". Suppose $C$ is an elliptic curve, with $c$ to be identity element under the group law. Suppose $f_t = id$, while $f_n$ is the multiply by $n$ morhpism(under the group law), they are not factor through an automorphism. | |
| Jun 1, 2014 at 0:58 | history | edited | Puzzled | CC BY-SA 3.0 |
added 124 characters in body
|
| Jun 1, 2014 at 0:51 | history | answered | Puzzled | CC BY-SA 3.0 |