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Título del libro: Vector Fields On Singular Varieties
Título del capítulo: The GSV Index

Autores UNAM:
JOSE ANTONIO SEADE KURI;
Autores externos:

Idioma:
Inglés
Año de publicación:
2009
Resumen:

One of the basic properties of the local Poincare-Hopf index is stability tinder perturbations. In other words, if a vector field has an isolated singularity oil an open set in R-n and if we perturb it slightly, then the Singularity may split into several singular points, with the property that the surn of the indices of the perturbed vector field at these singular points equals the index of the original vector field at its singularity If we now consider an analytic variety V defined by a holomorphic function f : (Cn+1, 0) -> (C, 0) with ail isolated critical point at 0, and if v is a vector field oil V, with ail isolated singularity at 0, then one may like "the index" of v at 0 to be stable tinder small perturbations of both, the function f and the vector field v. This leads naturally to another concept of index, called the GSV index, introduced by X. Gomez-Mont, J. Seade and A. Verjovsky in [71,144] for hypersurface germs, and extended in [147] (see also [149]) to complete intersecti


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