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Local aspects of singular F-theory compactifications for SUSY GUTmodel-building are fairly well understood in terms of Higgs bundles and theirspectral data. Several global issues remain, however, including a descriptionof G-fluxes, which are key to constructing chiral matter and stabilizingmoduli, and the global realization of U(1) symmetries that can forbidphenomenologically unfavorable couplings. In this paper, we sharpen our earlierproposal for describing G-fluxes through "spectral divisors" and introduce adistinguished "Tate divisor", which can be used to describe both G-flux andU(1)s when present. As an application, we give a general discussion ofM5-instanton contributions in the presence of G-flux and exemplify this in aconcrete example, where we comment on the ability of instanton inducedsuperpotential couplings to stabilize Kahler moduli.

On G-flux, M5 instantons, and U(1)s in F-theory