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.