Skip to main content
SpringerLink
Log in

Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets

  • Published:
Foundations of Computational Mathematics Aims and scope Submit manuscript

Abstract

In [8] counting complexity classes #PR and #PC 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 FPR #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 FPC #PC. We also obtain a corresponding completeness result for the Turing model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

  1. Deptartment of Mathematics, University of Paderborn, D-33095 Paderborn , Germany

    Peter Bürgisser & Martin Lotz

  2. Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

    Felipe Cucker

Authors
  1. Peter Bürgisser
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Felipe Cucker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Lotz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Peter Bürgisser, Felipe Cucker or Martin Lotz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bürgisser, P., Cucker, F. & Lotz, M. Counting Complexity Classes for Numeric Computations. III: Complex Projective Sets. Found Comput Math 5, 351–387 (2005). https://doi.org/10.1007/s10208-005-0146-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10208-005-0146-x

Search

Navigation