I am reading Ginsparg's Conformal Field Theory Notes and I am somewhat puzzled by the use of global and local. Specifically, I understand that the generators of two-dimensional conformal transformations are not globally defined on the Riemann sphere $C \cup \infty$, and the only globally defined Virasoro generators are $\{l_0, l_1, l_{-1}\}$ (and the corresponding antiholomorphic versions).
But at later stage (page 9) he says
Strictly speaking the only true conformal group in two dimensions is the projective (global) conformal group, since the remaining conformal transformations of (1.5) do not have global inverses on $C \cup \infty$.
What does he mean by "projective (global) conformal group"?
