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Prof. Dr. Martin Lotz
- © Martin Lotz
Mathematics Institute
Zeeman Building
University of Warwick
Coventry CV4 7AL
United Kingdom Persönliche Homepage
http://homepages.warwick.ac.uk/staff/Martin.Lotz/
Publikationen in der Arbeitsgruppe
| Citation key | BCL-Counting-Complexity-Classes-For-Numeric-Computations-Iii-Complex-Projective-Sets |
|---|---|
| Author | Peter Bürgisser and Felipe Cucker and Martin Lotz |
| Pages | 351-387 |
| Year | 2005 |
| Journal | Foundations of Computational Mathematics |
| Volume | 5 |
| Number | 4 |
| Abstract | In [Bürgisser & Cucker 2004a] counting complexity classes $\#P_R$ and $\#P_C$ in the Blum-Shub-Smale setting of computations over the real and complex numbers, respectively, were introduced. One of the main results of [Bürgisser & Cucker 2004a] is that the problem to compute the Euler characteristic of a semialgebraic set is complete in the class $FP_R^R}$. In this paper, we prove that the corresponding result is true over $\mathbb C$, namely that the computation of the Euler characteristic of an affine or projective complex variety is complete in the class $FP_C^C}$. We also obtain a corresponding completeness result for the Turing model. |
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