Yukawas, G-flux, and spectral covers from resolved Calabi-Yau's

We use the resolution procedure of Esole and Yau [1] to study Yukawa couplings, G-flux, and the emergence of spectral covers from elliptically fibered Calabi-Yau's with a surface of A(4) singularities. We provide a global description of the Esole-Yau resolution and use it to explicitly compute Chern classes of the resolved 4-fold, proving the conjecture of [2] for the Euler character in the process. We comment on the physical implications of the surprising singular fibers in codimension 2 and 3 in [1] and emphasize a group theoretic interpretation based on the A(4) weight lattice. We then construct explicit G-fluxes by brute force in one of the 6 birationally equivalent Esole-Yau resolutions, quantize them explicitly using our result for the second Chern class, and compute the spectrum and flux-induced 3-brane charges, finding agreement with results and conjectures of local models in all cases. Finally, we provide a precise description of the spectral divisor formalism in this setting and sharpen the procedure described in [3] in order to explicitly demonstrate how the Higgs bundle spectral cover of the local model emerges from the resolved Calabi-Yau geometry. Along the way, we demonstrate explicitly how the quantization rules for fluxes in the local and global models are related.