Bézout’s theorem states sufficient conditions (transversality) such that the intersection product of two algebraic curves inside an ambient algebraic surface gives literally the number of points at which the curves intersect.
This is the origin of intersection theory, see there for more.
The refinement of Bézout’s theorem for non-transversally intersecting varieties is Serre's intersection formula
Last revised on October 23, 2018 at 12:59:07. See the history of this page for a list of all contributions to it.