Arithmetic and string theory

We study M-Theory solutions with G-flux on the Fermat sextic Calabi-Yau fourfold, focusing on the relationship between the number of stabilized complex structure moduli and the tadpole contribution of the flux. We emphasize first the point-of-view from Hodge theory by using Griffith residues to compute the length of the flux with respect to the dimension of the Zariski tangent space, and we propose an alternative approach to check that those are the only results by making use of elementary number theory.