We extend one of the main results of Bürgisser and Cucker (http://www.arxiv.org/abs/cs/cs.CC/0312007, which asserts that the computation of the Euler characteristic of a semialgebraic set is complete in the counting complexity class FPℝ#Pℝ. The goal is to prove a similar result over ℂ: the computation of the Euler characteristic of an affine or projective complex variety is complete in the class FPℂ#Pℂ. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.
|Translated title of the contribution||The complexity to compute the Euler characteristic of complex varieties|
|Number of pages||5|
|Journal||Académie des Sciences. Comptes Rendus. Mathématique|
|Publication status||Published - 1 Sept 2004|