  Our goal is to convince the readers that the theory of complex normal surface
singularities can be a powerful tool in the study of numerical semigroups, and,
in the same time, a very rich source of interesting affine and numerical
semigroups. More precisely, we prove that the strongly flat semigroups, which
satisfy the maximality property with respect to the Diophantine Frobenius
problem, are exactly the numerical semigroups associated with negative definite
Seifert homology spheres via the possible 'weights' of the generic $S^1$-orbit.
Furthermore, we consider their generalization to the Seifert rational homology
sphere case and prove an explicit (up to a Laufer computation sequence) formula
for their Frobenius number. The singularities behind are the weighted
homogeneous ones, whose several topological and analytical properties are
exploited.
