  We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold
compactifications of F-theory, which in the local limit allow a spectral cover
description. The main tool of construction is the so-called spectral divisor in
the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs
bundle spectral cover. We exemplify the workings of this in the case of an E_6
singularity by constructing the resolved geometry, the spectral divisor and in
the local limit, the spectral cover. The G-flux constructed with the spectral
divisor is shown to be equivalent to the direct construction from suitably
quantized linear combinations of holomorphic surfaces in the resolved geometry,
and in the local limit reduces to the spectral cover flux.
