La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes

Details La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes

2004-05-26

arxiv.org/abs/math/0405491v2

Mathematics

Complex Variables

33 pages; minor grammatical changes; submitted to Annales de l'Institut Fourier

Scientific paper

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.

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