Localization Computation For Slightly Less Trivial P1 Target Example

Let \(X = \mathbb P^1\) and \(\beta = ([\mathbb P^1], g=0, u_1=u_2 = 0, u_3=1)\). Any stable log curve \((C,f, p_1,p_2,p_3)\) will have at most one non-contracted component by the degree \(1\) assumption and it must map identically to \(\mathbb P^1\). This means by stability we can have at most two contracted components.