Trace et calcul résiduel : une nouvelle version du théorème d’Abel inverse, formes abéliennes

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.