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

Martin Weimann
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Abstract

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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Martin Weimann. 2004-06-02. La trace via le calcul residuel: une nouvelle version du theoreme d'Abel-inverse, formes abeliennes. https://arxiv.org/abs/math/0405491

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