A method for computing Segre classes in arbitrary projective schemes

Corey Harris (FSU)

We give an algorithm for computing Segre classes of subschemes of arbitrary projective schemes. The algorithm relies on computing a contribution of the subscheme to the degree of the ambient scheme (embedded in projective space) and comparing this with the results from taking successive hyperplane sections. The result of these computations is a linear system of equations which determines the coefficients of the Segre class pushed forward to projective space. To our knowledge, this is the first algorithm to be able to compute Segre classes at large, in ambient schemes other than projective space or toric varieties. One application is that the algorithm may be used to implement a routine for computing intersection products of projective schemes.