  We present local classification results for isolated singularities of
functions with respect to a Nambu structure (multi-vector field) of maximal
degree, in a neighbourhood of a smooth point of its degeneracy hypersurface.
The results depend on a logarithmic version of the Brieskorn-Sebastiani
theorem, which guarantees the finiteness and freeness of the corresponding
deformation module. This relates the functional moduli of the classification
problem with the integrals of logarithmic forms along the vanishing cycles of
the complement of the Milnor fibers of the restriction of the function on the
degeneracy hypersurface of the Nambu structure, inside the Milnor fibers of the
function itself.
