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, Tome 58 (2008) no. 5, p. 1761-1783
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.
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.
DOI : https://doi.org/10.5802/aif.2398
Classification:  32S65,  14B05,  14Q10,  13D02,  13D25,  13H15,  32S25,  58K45
Mots 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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {58},
     number = {5},
     year = {2008},
     pages = {1761-1783},
     doi = {10.5802/aif.2398},
     mrnumber = {2445833},
     zbl = {1168.32023},
     language = {en},
     url = {http://www.numdam.org/item/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, Tome 58 (2008) no. 5, pp. 1761-1783. doi : 10.5802/aif.2398. http://www.numdam.org/item/AIF_2008__58_5_1761_0/

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