A direct algorithm to compute the topological Euler characteristic and Chern-Schwartz-MacPherson class of projective complete intersection varieties

Let V be a possibly singular scheme-theoretic complete intersection subscheme of Pn over an algebraically closed field of characteristic zero. Using a recent result of Fullwood (“On Milnor classes via invariants of singular subschemes”, Journal of Singularities) we develop an algorithm to compute the Chern-Schwartz-MacPherson class and Euler characteristic of V. This algorithm complements existing algorithms by providing performance improvements in the computation of the Chern-Schwartz-MacPherson class and Euler characteristic for certain types of complete intersection subschemes of Pn.