La complexité du calcul de la caractéristique d'Euler des variétés complexes

Peter Bürgisser; Felipe Cucker; Martin Lotz

doi:10.1016/j.crma.2004.06.008

La complexité du calcul de la caractéristique d'Euler des variétés complexes

Translated title of the contribution: The complexity to compute the Euler characteristic of complex varieties

Peter Bürgisser, Felipe Cucker, Martin Lotz

Research output: Contribution to journal › Article › peer-review

Abstract

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
Original language	French
Pages (from-to)	371-376
Number of pages	5
Journal	Académie des Sciences. Comptes Rendus. Mathématique
Volume	339
Issue number	5
DOIs	https://doi.org/10.1016/j.crma.2004.06.008
Publication status	Published - 1 Sept 2004

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http://dx.doi.org/10.1016/j.crma.2004.06.008

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abstract = "We extend one of the main results of B{\"u}rgisser 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. {\textcopyright} 2004 Acad{\'e}mie des sciences. Published by Elsevier SAS. All rights reserved.",

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AU - Cucker, Felipe

AU - Lotz, Martin

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N2 - 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.

AB - 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.

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DO - 10.1016/j.crma.2004.06.008

M3 - Article

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JO - Académie des Sciences. Comptes Rendus. Mathématique

JF - Académie des Sciences. Comptes Rendus. Mathématique

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La complexité du calcul de la caractéristique d'Euler des variétés complexes

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