Algébricité de germes analytiques.
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .
An interpolation theorem in toric varieties
In the spirit of a theorem of Wood, we give necessary and sufficient conditions for a family of germs of analytic hypersurfaces in a smooth projective toric variety to be interpolated by an algebraic hypersurface with a fixed class in the Picard group of .
Analytic curves in power series rings
Are the Isolated Singularities of Complete Intersections Determined by Their Singular Subspaces?