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H.-Ch. Graf von Bothmer; Wolfgang Ebeling; Xavier Gómez-Mont
An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
(Une formule algébrique pour l’indice d’un champ de vecteurs sur une singularité d’intersection complète isolée)
Annales de l'institut Fourier, 58 no. 5 (2008), p. 1761-1783, doi: 10.5802/aif.2398
Article PDF | Reviews MR 2445833 | Zbl 1168.32023
Class. Math.: 32S65, 14B05, 14Q10, 13D02, 13D25, 13H15, 32S25, 58K45
Keywords: Index, Vector Field, Complete Intersections, Complex, Homology of Complexes, Double Complexes, Homological Index, Buchsbaum-Eisenbud Theory

Résumé - Abstract

Let $(V,0)$ be a germ of a complete intersection variety in ${\mathbb{C}}^{n+k}$, $n>0$, having an isolated singularity at $0$ and $X$ be the germ of a holomorphic vector field having an isolated zero at $0$ and tangent to $V$. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of $X$ is also isolated in the ambient space ${\mathbb{C}}^{n+k}$ we give a formula for the homological index in terms of local linear algebra.


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