An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity
Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1761-1783.

Let (V,0) be a germ of a complete intersection variety in 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 n+k we give a formula for the homological index in terms of local linear algebra.

Soit (V,0) un germe d’intersection complète dans n+k , n>0, avec singularité isolée en 0 et soit X un germe de champs de vecteurs holomorphes en n+k tangents à V et qui a une singularité isolée dans V en 0. Nous montrons que dans ce cas l’indice homologique et l’indice GSV coïncident. Dans le cas où le zéro de X est aussi isolé dans l’espace ambiant n+k , nous donnons une formule pour l’indice homologique en terme de l’algèbre linéaire locale.

DOI: 10.5802/aif.2398
Classification: 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
Bothmer, H.-Ch. Graf von 1; Ebeling, Wolfgang 1; Gómez-Mont, Xavier 2

1 Leibniz Universität Hannover Institut für Algebraische Geometrie Postfach 6009 30060 Hannover (Germany)
2 CIMAT A.P. 402 Guanajuato, 36000 (México)
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Bothmer, H.-Ch. Graf von; Ebeling, Wolfgang; Gómez-Mont, Xavier. An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1761-1783. doi : 10.5802/aif.2398. https://aif.centre-mersenne.org/articles/10.5802/aif.2398/

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