The complexity to compute the Euler characteristic of complex varieties (Q1886973)

\textit{P. Bürgisser} and \textit{F. Cucker} [J. Complexity 22, No. 2, 147--191 (2006; Zbl 1149.68029)] proved that the computation of the Euler characteristic of a semialgebraic set is complete in the counting class \(FP_{\mathbb R}^{\sharp P_{\mathbb R}}.\) In the paper under review, the authors prove that the computation of the Euler characteristic of an affine or projective complex variety is complete in the class \(FP_{\mathbb C}^{\sharp P_{\mathbb C}}.\)