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Comptes Rendus Mathématique
Volume 339, n° 5
pages 371-376 (septembre 2004)
Doi : 10.1016/j.crma.2004.06.008
Received : 7 June 2004 ;  accepted : 14 June 2004
The complexity to compute the Euler characteristic of complex varieties
La complexité du calcul de la caractéristique dʼEuler des variétés complexes.
 

Peter Bürgisser a, 1 , Felipe Cucker b, 2 , Martin Lotz a, 1
a Institute of Mathematics, University of Paderborn, 33095 Paderborn, Germany 
b Department of Mathematics, City University of Hong Kong, 83, Tat Chee Avenue, Kowloon, Hong Kong 

Abstract

We extend one of the main results of Bürgisser and Cucker (0312007), which asserts that the computation of the Euler characteristic of a semialgebraic set is complete in the counting complexity class  . The goal is to prove a similar result over  : the computation of the Euler characteristic of an affine or projective complex variety is complete in the class  . To cite this article: P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
Résumé

Dans cette Note, nous étendons un des résultats principaux de Bürgisser et Cucker (0312007), qui établit que le calcul de la caractéristique dʼEuler dʼun ensemble semialgébrique est complet dans la classe de complexité de comptage  . Nous prouvons un résultat similaire sur   : le calcul de la caractéristique dʼEuler dʼune variété algébrique (affine ou projective) est complet dans la classe  . Pour citer cet article : P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).

The full text of this article is available in PDF format.
1  Partially supported by DFG grant BU 1371.
2  Partially supported by City University SRG grant 7001558.


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