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Título del libro: Vector Fields On Singular Varieties
Título del capítulo: The Homological Index and Algebraic Formulas

Autores UNAM:
JOSE ANTONIO SEADE KURI;
Autores externos:
Idioma:
Inglés
Año de publicación:
2009
Resumen:

We have already defined and studied several indices of vector fields on singular varieties. each of them being related to some property of the index of Poincare-Hopf, or to some extension of the tangent bundle to the case of singular varieties. There is another line of research with remarkable works by various authors, that originates in the well-known fact (cf. Example 1.6.2) that for a holomorphic vector field v in C-n with all isolated singularity at 0, the local Poincare-Hopf index satisfies: Ind(PH)(v, 0) = dim O-Cn,O-0/(a(1),...,a(n)), (7.0.1) where (a(1),...,a(n)) is the ideal generated by the components of v. In the real analytic setting, the equivalent statement is given by the formula of Eisenbud-Levin-Khimshiashvili, expressing the local Poincare-Hopf index through the signature of a certain quadratic form. These facts motivated the search for algebraic formulas for indices of vector fields on singular varieties. A majors contribution in this direction was given by V. I. Arn

Entidades citadas de la UNAM:
Fuente:



ISBN:
9783642052040
Editorial:
SPRINGER-VERLAG BERLIN

Tipo de producto:
Article



DOI:
10.1007/978-3-642-05205-7_7