Intersection multiplicity is a numerical invariant that measures how many times two algebraic varieties intersect at a given point, taking into account both the dimensions and local behavior of the varieties near that point. It helps to understand the local structure of the varieties and their intersections, reflecting both algebraic and geometric properties. This concept is essential in studying projective varieties and offers insights into the properties of normal and Cohen-Macaulay varieties as well.
congrats on reading the definition of Intersection Multiplicity. now let's actually learn it.