Let be a germ of a complete intersection variety in , , having an isolated singularity at and be the germ of a holomorphic vector field having an isolated zero at and tangent to . We show that in this case the homological index and the GSV-index coincide. In the case when the zero of is also isolated in the ambient space we give a formula for the homological index in terms of local linear algebra.
Soit un germe d’intersection complète dans , , avec singularité isolée en et soit un germe de champs de vecteurs holomorphes en tangents à et qui a une singularité isolée dans en . Nous montrons que dans ce cas l’indice homologique et l’indice GSV coïncident. Dans le cas où le zéro de est aussi isolé dans l’espace ambiant , nous donnons une formule pour l’indice homologique en terme de l’algèbre linéaire locale.
Keywords: Index, Vector Field, Complete Intersections, Complex, Homology of Complexes, Double Complexes, Homological Index, Buchsbaum-Eisenbud Theory
Mot clés : indice, champ de vecteur, intersection complète, complexe, homologie de complexes, double complexes, indice homologique, théorie Buchsbaum-Eisenbud
@article{AIF_2008__58_5_1761_0, author = {Bothmer, H.-Ch. Graf von and Ebeling, Wolfgang and G\'omez-Mont, Xavier}, title = {An {Algebraic} {Formula} for the {Index} {of~a~Vector} {Field} on an {Isolated} {Complete} {Intersection} {Singularity}}, journal = {Annales de l'Institut Fourier}, pages = {1761--1783}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {5}, year = {2008}, doi = {10.5802/aif.2398}, zbl = {1168.32023}, mrnumber = {2445833}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.2398/} }
TY - JOUR AU - Bothmer, H.-Ch. Graf von AU - Ebeling, Wolfgang AU - Gómez-Mont, Xavier TI - An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity JO - Annales de l'Institut Fourier PY - 2008 SP - 1761 EP - 1783 VL - 58 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2398/ DO - 10.5802/aif.2398 LA - en ID - AIF_2008__58_5_1761_0 ER -
%0 Journal Article %A Bothmer, H.-Ch. Graf von %A Ebeling, Wolfgang %A Gómez-Mont, Xavier %T An Algebraic Formula for the Index of a Vector Field on an Isolated Complete Intersection Singularity %J Annales de l'Institut Fourier %D 2008 %P 1761-1783 %V 58 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2398/ %R 10.5802/aif.2398 %G en %F AIF_2008__58_5_1761_0
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. http://archive.numdam.org/articles/10.5802/aif.2398/
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