Consider a symplectic manifold $(M,\omega)$ with the property that $\pi_2(M) = 0$. Given a time dependent hamiltonian $H_t$ on $M$, and a $\omega$-compatible almost complex structure J on M, we may look at smooth,contractible finite energy solutions to the floer equation. Let

$$\mathscr{M}:=\{ u:\mathbb{R} \times S^1|\text{u is contractible and is solution of the Floer equation with finite energy}\}$$

It can be shown that $\mathscr{M}$ is compact with respect to $C^\infty$ uniform convergence on compact sets topology. Also $\mathbb{R}$ acts on $\mathscr M$ by reparametrization.

On the other hand we may fix a homology class $A \in H_2(M)$ which is indecomposable ( meaning that we cannot get homology classes $B$ and $C$ in $H_2(M)$ such that $A= B +C$ such that $\omega(B) > 0$ and $\omega(C) > 0$) on $M$ and consider the moduli space of J-holomorphic spheres in the class A. Let us denote this moduli space by $\mathscr{M}^\prime$

This space on the other hand is not compact but if we look at the space of unparametrised J-spheres i.e ${\mathscr{M^\prime}} / {PSL(2,\mathbb{C}})$ then the space becomes compact(As $PSL(2,\mathbb{C})$ is the automorphism group for a sphere) . This means that given a sequence $u_k \in \mathscr{M^\prime}$ there is a sub sequence $u_{k^\prime}$ that converges to a unparametrised curve $u \in {\mathscr{M^\prime}} / {PSL(2,\mathbb{C}})$.

Given that we may think of the Cauchy Riemann equation as the Floer equation when the time dependent hamiltonian are constant, why are we able to recover the parametrization of the limiting curve in the Floer case but not able to recover the parametrization in the case of a J-holomorphic sphere? Is there any fundamental reason connected to how the reparameterization groups acts on the moduli spaces that makes this happen?