The Witten complex for algebraic curves with cone-like singularities

Ursula Ludwig

doi:10.1016/j.crma.2009.03.027

Differential Geometry

The Witten complex for algebraic curves with cone-like singularities

Presented by: Jean-Michel Bismut

Ursula Ludwig ¹

¹ Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany

Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 651-654.

Abstract
Résumé

The Witten deformation is an analytical method proposed by Witten which, given a function $f : M \to R$ 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.

Soit M une variété Riemannienne compacte et soit $f : M \to R$ 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.

Received: 2009-01-12
Accepted: 2009-03-24
Published online: 2009-04-24

DOI: 10.1016/j.crma.2009.03.027

Author's affiliations:

Ursula Ludwig ¹

¹ Mathematisches Institut, Eckerstrasse 1, 79104 Freiburg, Germany

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     title = {The {Witten} complex for algebraic curves with cone-like singularities},
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Ursula Ludwig. The Witten complex for algebraic curves with cone-like singularities. Comptes Rendus. Mathématique, Volume 347 (2009) no. 11-12, pp. 651-654. doi : 10.1016/j.crma.2009.03.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.027/

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