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

Autores UNAM:
JOSE ANTONIO SEADE KURI;
Autores externos:

Idioma:
Inglés
Año de publicación:
2009
Resumen:

The constructions described in the previous chapter, mostly based on [31, 33, 139], provide geometric insights of the Schwartz-MacPherson classes via obstruction theory and localization. These approaches are useful for understanding what the classes measure from the viewpoint of indices of vector fields and frames. The Fulton-Johnson classes [59,60] provide another way of generalizing the Chern class of complex manifolds to the case of singular varieties. In the context we consider, they coincide with the virtual classes (see Sect. 11.1). In this chapter we define and study the virtual classes from a viewpoint similar to the one we used in the previous chapter for the Schwartz-MacPherson classes. This is based on our articles [31, 34), joint work with D. Lehmann. If the variety V is globally defined by a function on AY, the virtual classes can be localized topologically and one can interpret them as "weighted" Schwartz classes. That is explained in Sect. 11.3 where we prove the Proport


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