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Título del libro: Vector Fields On Singular Varieties
Título del capítulo: Milnor Number and Milnor Classes

Autores UNAM:
JOSE ANTONIO SEADE KURI;
Autores externos:

Idioma:
Inglés
Año de publicación:
2009
Resumen:

Both Schwartz-MacPherson and Fulton-Johnson classes generalize Chern classes to the case of singular varieties. It is known that for local complete intersections with isolated singularities, the 0-degree SM and FJ classes differ by the local Milnor numbers [149] and all other classes coincide [155]. As we explain in the sequel, if V has nonisolated singularities, the, difference c(i)(SM)(V) - c(i)(FJ)(V) of the SM and FJ classes is, for each i, a homology class with support in the homology H-2i(Sing(V)) of the singular set of V. That is the reason for which their difference was called in [30,31] the Milnor class of degree i. These classes have been also considered, from different viewpoints, by other authors, most notably by P. Aluffi, T. Ohmoto, A. Parusinski, P. Pragacz, J. Schurmann, S. Yokura. In this chapter we introduce the Milner classes of a local complete intersection V of dimension n >= 1 in a complex manifold M, defined by a, regular sections of a holomorphic bundle N over M


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