  We show here how residue calculus (residue currents, Grothendieck residues,
duality theorem) can be used to obtain an algebraic characterization of the
Abel-transform of a meromorphic form on germs of analytic sets. We prove by
this way a stronger version of Abel-inverse theorem with an "algebraic"
approach and we show the link with Wood's theorem. Furthermore, we obtain a new
method to bound easily the dimension of the vector space of abelian forms on an
algebraic projective hypersurface.
