David Eklund: A method to compute the degrees of the Chern classes of a smooth variety

Let Z ⊂ ℙ^r be a smooth connected variety. Suppose that Z is realized as a connected component of the intersection of r hypersurfaces. The contribution of Z to the Bezout number of the intersection is called the equivalence of Z. The equivalence may be computed with numerical homotopy methods, as well as computer algebra. An intersection theoretic result relates the equivalence of Z to the Chern classes of Z, which leads to a method to compute the degrees of the Chern classes. I will also discuss how this procedure generalizes to compute intersection numbers of Chern classes.