Abstract
We show here how residue calculus (residue currents, Grothendieck residues, duality theorem) can be used to obtain an 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 projective hypersurface.
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