The Witten complex for algebraic curves with cone-like singularities

Abstract

The Witten deformation is an analytical method proposed by Witten which, given a function f : M → 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. To cite this article: U. Ludwig, C. R. Acad. Sci. Paris, Ser. I 347 (2009).