Relative Brauer groups II.
A relativization of earlier constructions and Nori’s rational Lefschetz theorem enable interesting examples of the “topological filtration” on algebraic cycles.
Let be a polynomial dominating map from to . We study the quotient of polynomial 1-forms that are exact along the generic fibres of , by 1-forms of type , where are polynomials. We prove that is always a torsion -module. Then we determine under which conditions on we have . As an application, we study the behaviour of a class of algebraic -actions on , and determine in particular when these actions are trivial.
The purpose of this paper is to give a characterization of the relative tangent cone of two analytic curves in with an isolated intersection.
We give a characterization of the relative tangent cone of an analytic curve and an analytic set with an improper isolated intersection. Moreover, we present an effective computation of the intersection multiplicity of a curve and a set with s-metrization.