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We study M-Theory solutions with $G$-flux on the Fermat sextic Calabi-Yaufourfold, focussing on the relationship between the number of stabilizedcomplex structure moduli and the tadpole contribution of the flux. We use twoalternative approaches to define the fluxes: algebraic cycles and(appropriately quantized) Griffiths residues. In both cases, we collectevidence for the non-existence of solutions which stabilize all moduli and staywithin the tadpole bound

More on $G$-flux and General Hodge Cycles on the Fermat Sextic