Dans cette Note, nous étendons un des résultats principaux de Bürgisser et Cucker (http://www.arxiv.org/abs/cs/cs.CC/0312007), qui établit que le calcul de la caractéristique d'Euler d'un ensemble semialgébrique est complet dans la classe de complexité de comptage . Nous prouvons un résultat similaire sur : le calcul de la caractéristique d'Euler d'une variété algébrique (affine ou projective) est complet dans la classe .
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 . 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 .
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@article{CRMATH_2004__339_5_371_0, author = {B\"urgisser, Peter and Cucker, Felipe and Lotz, Martin}, title = {The complexity to compute the {Euler} characteristic of complex varieties}, journal = {Comptes Rendus. Math\'ematique}, pages = {371--376}, publisher = {Elsevier}, volume = {339}, number = {5}, year = {2004}, doi = {10.1016/j.crma.2004.06.008}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2004.06.008/} }
TY - JOUR AU - Bürgisser, Peter AU - Cucker, Felipe AU - Lotz, Martin TI - The complexity to compute the Euler characteristic of complex varieties JO - Comptes Rendus. Mathématique PY - 2004 SP - 371 EP - 376 VL - 339 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.06.008/ DO - 10.1016/j.crma.2004.06.008 LA - en ID - CRMATH_2004__339_5_371_0 ER -
%0 Journal Article %A Bürgisser, Peter %A Cucker, Felipe %A Lotz, Martin %T The complexity to compute the Euler characteristic of complex varieties %J Comptes Rendus. Mathématique %D 2004 %P 371-376 %V 339 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.06.008/ %R 10.1016/j.crma.2004.06.008 %G en %F CRMATH_2004__339_5_371_0
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin. The complexity to compute the Euler characteristic of complex varieties. Comptes Rendus. Mathématique, Tome 339 (2004) no. 5, pp. 371-376. doi : 10.1016/j.crma.2004.06.008. http://www.numdam.org/articles/10.1016/j.crma.2004.06.008/
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