Counting complexity classes for numeric computations. III : Complex projective sets

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)351-387
Journal / PublicationFoundations of Computational Mathematics
Issue number4
Publication statusPublished - Nov 2005


In [8] counting complexity classes #P and #P in the Blum-Shub-Smale (BSS) setting of computations over the real and complex numbers, respectively, were introduced. One of the main results of [8] is that the problem to compute the Euler characteristic of a semialgebraic set is complete in the class FP #Pℝ. In this paper, we prove that the corresponding result is true over ℂ, namely that the computation of the Euler characteristic of an affine or projective complex variety is complete in the class FP #Pℂ. We also obtain a corresponding completeness result for the Turing model. © 2005 SFoCM.

Research Area(s)

  • Complexity classes, Counting problems, Euler characteristic