An algorithm to compute certain euler characteristics and Chern-Schwartz-MacPherson classes

Abstract

Let V be a possibly singular scheme-theoretic global complete intersection subscheme of Pⁿ and assume that V can be written as the intersection of j hypersurfaces such that the intersection of j -- 1 of the hypersurfaces is smooth (scheme theoretically). Using a result of Fullwood [5] we develop a probabilistic algorithm to compute the Chern-Schwartz-MacPherson class (c_SM) and Euler characteristic of V. This algorithm complements existing algorithms by providing performance improvements in the computation of the c_SM class and Euler characteristic for schemes having the special structure described above.