Regularizations of residue currents

Residue Currents of Holomorphic Morphisms

Given a generically surjective holomorphic vector bundle morphism f : E → Q, E and Q Hermitian bundles, we construct a current R with values in Hom (Q,H), where H is a certain derived bundle, and with support on the set Z where f is not surjective. The main property is that if φ is a holomorphic section of Q, and Rφ = 0, then locally fψ = φ has a holomorphic solution ψ. In the generic case also...

Ideals of Smooth Functions and Residue Currents

Let f = (f 1 ; : : : ; f m) be a holomorphic mapping in a neighborhood of the origin in C n. We nd suucient condition, in terms of residue currents, for a smooth function to belong to the ideal in C k generated by f. If f is a complete intersection the condition is essentially necessary. More generally we give suucient condition for an element of class C k in the Koszul complex induced by f to ...

Trace, residue currents and multidimensional residues, duality and division

Averaging residue currents and the Stückrad-Vogel algorithm

Trace formulas (Lagrange, Jacobi-Kronecker, Bergman-Weil) play a key role in division problems in analytic or algebraic geometry (including arithmetic aspects, see for example [10]). 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 Cro...

Vector optimization: Singularities, regularizations

We discuss three scalarizations of the multiobjective optimization from the point of view of the parametric optimization. We analize three important aspects: i) What kind of singularities may appear in the diierent parametriza-tions ii) Regularizations in the sense of Jongen, Jonker and Twilt, and in the sense of Kojima and Hirabayashi. iii) The Mangasarian-Fromovitz Constraint Qualiication for...