Timeline for Computations in the Deligne-Mumford compactification with marked points
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2010 at 15:10 | comment | added | stankewicz | Even better start with $g=0$ and $n=4$ so your moduli space is $\mathbb{P}^1$, given by the cross-ratio $\lambda$ of those points, so we may as well fix the first 3 in order as $0,1,\infty$. Once we do that there are no automorphisms of this pointed curve. If $\lambda$ collides with one of them, we have automorphisms so we have to blow up that (unstable) point. We are left then with 2 $\mathbb{P}^1$'s with 2 marked points meeting at a distinct point. $$ $$ For larger $n$ you just perform that sort of operation many times. For larger $g$ you might have automorphisms of the pointed curve. | |
| Dec 15, 2010 at 8:40 | comment | added | Dr Shello | @Andy: Could you provide a sketch of the ideas here? | |
| Nov 22, 2010 at 6:40 | comment | added | Andy Putman | @Alex : I recommend learning what is going on first in the case $g=0$, where things are easier. For this, I recommend reading Chapter 1 of Kock-Vainsencher's "An invitation to quantum cohomology". | |
| Nov 22, 2010 at 5:16 | comment | added | Alex | Could you provide more details? For example, how do you determine what the components look like and how many components there are? | |
| Nov 22, 2010 at 4:40 | history | answered | Sándor Kovács | CC BY-SA 2.5 |