  We revisit the issue of M5-brane instanton corrections to the superpotential
in F-theory compactifications on elliptically fibered Calabi-Yau fourfolds.
Elaborating on concrete geometries, we compare the instanton zero modes for
non-perturbative F-theory models with the zero modes in their perturbative Sen
limit. The fermionic matter zero modes localized on the intersection of the
instanton with the space-time filling D7-branes show up in a geometric way in
F-theory. Methods for their computation are developed and, not surprisingly,
exceptional gauge group structures do appear. Finally, quite intriguing
geometrical aspects of the one-loop determinant are discussed.
