Lʼindice des champs de vecteurs sur les courbes de Cohen–Macaulay

Abstract

In this paper a new method for computing the topological index of a vector field at Cohen–Macaulay curves is described. It is based on properties of regular meromorphic differential forms which are used for computing the homological index of vectors fields introduced by X. Gómez-Mont. In particular, we show how to compute the index at quasihomogeneous Gorenstein curves and complete intersections, at monomial curves, at Cohen–Macaulay space curves, and others. In contrast to previous articles on this subject we do not use the technique of spectral sequences, or computer algebra systems for symbolic calculations.