Lê cycles and Milnor classes
Por:
Callejas-Bedregal R., Morgado M.F.Z., Seade J.
Publicada:
1 ago 2014
Categoría:
Mathematics (miscellaneous)
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.
Filiaciones:
Callejas-Bedregal R.:
Centro de Ciências Exatas e da Natureza-Campus I, Universidade Federal da Paraíba-UFPb, Cidade Universitária s/n Castelo Branco, João Pessoa, PB, Brazil
Morgado M.F.Z.:
Instituto de Biociências Letras e Ciências Exatas, Universidade Estadual Paulista-UNESP, Rua Cristóvão Colombo, 2265, Jd. Nazareth, S.J. do Rio Preto, SP, Brazil
Seade J.:
Instituto de Matemáticas, Unidad Cuernavaca, Universidad Nacional Autónoma de México-UNAM, Av. Universidad s/n, Lomas de Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico
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