An algorithm for computing the topological Euler characteristic of complex projective varieties

Abstract

We present an algorithm for the symbolic and numerical computation of the degrees of the Chern-Schwartz-MacPherson classes of a closed subvariety of projective space P^n. As the degree of the top Chern-Schwartz-MacPherson class is the topological Euler characteristic, this also yields a method to compute the topological Euler characteristic of projective varieties. The method is based on Aluffi's symbolic algorithm to compute degrees of Chern-Schwartz-MacPherson classes, a symbolic method to compute degrees of Segre classes, and the regenerative cascade by Hauenstein, Sommese and Wampler. The new algorithm complements the existing algorithms. We also give an example for using a theorem by Huh to compute an invariant from algebraic statistics, the maximum likelihood degree of an implicit model.

10 pages

References in corpus (2)

• The maximum likelihood degree of a very affine variety
• A Macaulay2 package for characteristic classes and the topological Euler characteristic of complex projective schemes

Cited by in corpus (5)

• An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties
• A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties
• Computing characteristic classes of subschemes of smooth toric varieties
• A Macaulay2 package for characteristic classes and the topological Euler characteristic of complex projective schemes
• Combinatorial Excess Intersection