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Título del libro: Vector Fields On Singular Varieties
Título del capítulo: Characteristic Classes of Coherent Sheaves on Singular Varieties

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

As we have seen along this book, for a singular variety V, there are several definitions of Chern classes, the Mather class, the Schwartz-MacPherson class, the Fulton-Johnson class and so forth. They are in the homology of V and, if V is nonsingular, they all reduce to the Poincare dual of the Chern class c*(TV) of the tangent bundle TV of V. On the other hand, for a coherent sheaf F on V, the (cohomology) Chern character ch*(F) or the Chern class c*(F) makes sense if either V is nonsingular or F is locally free. In this chapter, we propose a definition of the homology Chern character ch(*)(F) or the Chern class c(*)(F) for a coherent sheaf F on a possibly singular variety V. In this direction, the homology Chern character or the Chern class is defined in [140] (see also [100]) using the Nash type modification of V relative to the linear space associated to the coherent sheaf T. Also, the homology Todd class tau(F) is introduced in [15] to describe their Riemann-Roch theorem. Our class

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Fuente:



ISBN:
9783642052040
Editorial:
SPRINGER-VERLAG BERLIN

Tipo de producto:
Article



DOI:
10.1007/978-3-642-05205-7_13