Publishing house / Journals and Serials / Colloquium Mathematicum / All issues

Abstract

We present a formula for the intersection multiplicity of the images of two subvarieties under an etale morphism between smooth varieties over a field k. It is a generalization of Fulton's Example 8.2.5 from [3], where a strong additional assumption has been imposed. In a special case where the base field k is algebraically closed and a proper component of the intersection is a closed point, intersection multiplicity is an invariant of etale morphisms. This corresponds with analytic geometry where intersection multiplicity is an invariant of local biholomorphisms.