Bézout’s theorem (Algebraic Geometry)

The classic version of Bézout’s theoremMathworldPlanetmath states that two complex projective curves of degrees m and n which share no common component intersect in exactly mn points if the points are counted with multiplicityMathworldPlanetmath.

The generalized version of Bézout’s theorem states that if A and B are algebraic varieties in k-dimensional projective space over an algebraically complete field and AB is a varietyMathworldPlanetmathPlanetmath of dimension dim(A)+dim(B)-k, then the degree of AB is the productPlanetmathPlanetmath of the degrees of A and B.

Title Bézout’s theorem (Algebraic GeometryMathworldPlanetmathPlanetmathPlanetmath)
Canonical name BezoutsTheoremAlgebraicGeometry
Date of creation 2013-03-22 14:36:45
Last modified on 2013-03-22 14:36:45
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 9
Author rspuzio (6075)
Entry type Algorithm
Classification msc 14A10