Timeline for actual dimension of concrete moduli space of holomorphic curves vs its virtual dimension
Current License: CC BY-SA 3.0
5 events
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| May 19, 2015 at 16:53 | comment | added | Agustín Moreno | Oh, ok. That makes more sense... terminology failed me. Sure, if you fix $0$ and $\infty$ to be your branch points, and look at the maps that fix these two points and ramify at them to order 2, then they are of the form $z \mapsto az^2$, which up to reparametrization (i.e dilation) is just the map $z^2$. If you now have two other different ramifying points, take an automorphism mapping them to $0$ and $\infty$, and so, precomposing with it (and a dilation, if necessary) you get the map $z^2$ again. I.e the branch points determine your map up to parametrization, and now I am happy. | |
| May 19, 2015 at 16:06 | comment | added | Chris Gerig | The branch points are in the image; it's the critical values that you're really counting. | |
| May 19, 2015 at 9:54 | comment | added | Agustín Moreno | Fair enough. But say, why is it true that if you have two maps with different branch points, then they do not differ by an automorphism preserving these points? I want to make sure I am not counting more things...That is what I dont see. | |
| May 18, 2015 at 12:57 | history | edited | Agustín Moreno | CC BY-SA 3.0 |
deleted 679 characters in body
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| May 18, 2015 at 12:15 | history | answered | Agustín Moreno | CC BY-SA 3.0 |