Artículos de revistas
Lê cycles and Milnor classes
Fecha
2013-01-18Registro en:
Inventiones Mathematicae, p. 1-30.
0020-9910
1432-1297
10.1007/s00222-013-0450-7
2-s2.0-84872266136
Autor
Universidade Federal da Paraíba (UFPB)
Universidade Estadual Paulista (Unesp)
Universidad Nacional Autónoma de México-UNAM
Institución
Resumen
The purpose of this work is to establish a link between the theory of Chern classes for singular varieties and the geometry of the varieties in question. Namely, we show that if Z is a hypersurface in a compact complex manifold, defined by the complex analytic space of zeroes of a reduced non-zero holomorphic section of a very ample line bundle, then its Milnor classes, regarded as elements in the Chow group of Z, determine the global Lê cycles of Z; and vice versa: The Lê cycles determine the Milnor classes. Morally this implies, among other things, that the Milnor classes determine the topology of the local Milnor fibres at each point of Z, and the geometry of the local Milnor fibres determines the corresponding Milnor classes. © 2013 Springer-Verlag Berlin Heidelberg.