When defining (Hamiltonian) Floer homology, one requires the symplectic manifold $(M,\omega)$ to be (weakly) monotone, i.e. the Chern class is positively proportional to the symplectic area. This ensures that generically no $J$-holomorphic spheres with negative Chern number exist. Can somebody elaborate (in some detail) on why such spheres are a problem in the compactification of the space of Floer trajectories?
More generally, the monotonicity condition is supposed to obstruct the existence of sphere bubbles. I am a bit confused on how this is implied by monotonicity.