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

Martin Weimann (1)

1 LaBAG - Laboratoire Bordelais d'Analyse et Géométrie

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.

Domaines: Variables complexes [math.CV]; Algèbre commutative [math.AC]

Martin Weimann. La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes. 2004. ⟨hal-00011172⟩