Averaging residue currents and the Stückrad-Vogel algorithm

Alain Yger (1)

1 IMB - Institut de Mathématiques de Bordeaux

Trace formulas (Lagrange, Jacobi-Kronecker, Bergman-Weil) play a key role in division problems in analytic or algebraic geometry (including arithmetic aspects. Unfortunately, they usually hold within the restricted frame of complete intersections. Besides the fact that it allows to carry local or semi global analytic problems to a global geometric setting (think about Crofton's formula), averaging the Cauchy kernel in order to get the Bochner-Martinelli kernel leads to the construction of explicit candidates for the realization of Grothendieck's duality, namely BM residue currents, extending thus the cohomological incarnation of duality which appears in the complete intersection or Cohen-Macaulay cases. We recall here such constructions and, in parallel, suggest how far one could take advantage of the multiplicative inductive construction introduced in by N. Coleff and M. Herrera, by relating it to the Stückrad-Vogel algorithm developed towards improper intersection theory. This presentation relies deeply on a recent collaboration with M. Andersson, H. Samuelsson and E. Wulcan in Göteborg.

Mots clés: Residual currents; Intersection theory

Domaines: Variables complexes [math.CV]

Alain Yger. Averaging residue currents and the Stückrad-Vogel algorithm. 2011. ⟨hal-00601678v3⟩