  Linear global modes, which are time-harmonic solutions with vanishing
boundary conditions, are analysed in the context of the complex Ginzburg-Landau
equation with slowly varying coefficients in doubly infinite domains. The most
unstable modes are shown to be characterized by the geometry of their Stokes
line network: they are found to generically correspond to a configuration with
two turning points issued from opposite sides of the real axis which are either
merged or connected by a common Stokes line. A region of local absolute
instability is also demonstrated to be a necessary condition for the existence
of unstable global modes.
