[Le complexe de Witten sur des courbes algébriques complexes à singularités coniques]
Soit M une variété Riemannienne compacte et soit une fonction de Morse sur M. La méthode de Witten utilise une déformation du complexe de de Rham pour démontrer les inegalités de Morse. Le but de cette Note est d'étendre cette méthode au cas des courbes algébriques complexes à singularités coniques, munis de fonctions appelées fonctions de Morse admissibles. Ces fonctions sont des fonctions de Morse stratifiées au sens de la théorie de Goresky/MacPherson.
The Witten deformation is an analytical method proposed by Witten which, given a function on a smooth compact Riemannian manifold M, leads to a proof of the Morse inequalities. In this Note we generalise the Witten deformation to singular complex algebraic curves X with cone-like singularities, and functions on X which we call admissible Morse functions. They are particular examples of stratified Morse functions in the sense of the theory developed by Goresky/MacPherson.
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@article{CRMATH_2009__347_11-12_651_0,
author = {Ludwig, Ursula},
title = {The {Witten} complex for algebraic curves with cone-like singularities},
journal = {Comptes Rendus. Math\'ematique},
pages = {651--654},
publisher = {Elsevier},
volume = {347},
number = {11-12},
year = {2009},
doi = {10.1016/j.crma.2009.03.027},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2009.03.027/}
}
TY - JOUR AU - Ludwig, Ursula TI - The Witten complex for algebraic curves with cone-like singularities JO - Comptes Rendus. Mathématique PY - 2009 SP - 651 EP - 654 VL - 347 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2009.03.027/ DO - 10.1016/j.crma.2009.03.027 LA - en ID - CRMATH_2009__347_11-12_651_0 ER -
%0 Journal Article %A Ludwig, Ursula %T The Witten complex for algebraic curves with cone-like singularities %J Comptes Rendus. Mathématique %D 2009 %P 651-654 %V 347 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2009.03.027/ %R 10.1016/j.crma.2009.03.027 %G en %F CRMATH_2009__347_11-12_651_0
Ludwig, Ursula. The Witten complex for algebraic curves with cone-like singularities. Comptes Rendus. Mathématique, Tome 347 (2009) no. 11-12, pp. 651-654. doi : 10.1016/j.crma.2009.03.027. http://www.numdam.org/articles/10.1016/j.crma.2009.03.027/
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