I was wondering if I could ask about stable $n$-pointed curves (essentially intersecting copies of $\mathbb{P}^1$ with at least $3$ special points on each copy - these may be either a point of intersection or a marked point).
I was wondering whether someone could perhaps help me by sketching out the possible cases for stable $6$-pointed curves? I have found all the cases possible for $5$ marked points (see sketch below), but I lose track in terms of the types of intersections that may occur for $3$ components and beyond in the case of $6$ marked points.
I have for $n=6$:
1 component: analogous to $n=5$
2 components: $2$ potential cases (distributing the marks by $2,4$ or $3,3$).
3 components: where I find difficulty.
$n=5$" />Would it be possible to construct the same sketch but for the case $n=6$?
Thanks you very much in advance!
I think I've found the sketches for stable $6$-pointed curves. I was getting confused as I was forgetting the no closed circuits condition.
Thanks to @Tabes Bridges for their help!