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

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

The virtual index was first introduced in [111] by D. Lehmann, M. Soares and T. Suwa for holomorphic vector fields; the extension to continuous vector fields is immediate and has been done in [30, 31, 149]. If the variety has only isolated singularities, the virtual index and the GSV index coincide. The virtual index has several interesting features, as for instance that it is relatively easy to compute when the vector field we deal with is holomorphic, and also that it is defined for vector fields with singular set a compact set of arbitrary dimension. In this chapter we introduce the virtual index in the context of singular varieties V which are local complete intersections defined by a section of a, holomorphic vector bundle N over a complex manifold M (see Sect. 5.1 below). The virtual tangent bundle is then defined as (TM - N)|(V), where TM denotes the holomorphic tangent bundle of M. One can think of the virtual index as being a localization of the top dimensional Chern class of

Entidades citadas de la UNAM:
Fuente:



ISBN:
9783642052040
Editorial:
SPRINGER-VERLAG BERLIN

Tipo de producto:
Article



DOI:
10.1007/978-3-642-05205-7_5