Le cycles and Milnor classes

• 成果类型: Article
• 署名作者: Callejas-Bedregal, R.; Morgado, M. F. Z.; Seade, J.
• 署名单位: Universidade Federal da Paraiba; Universidade Estadual Paulista; Universidad Nacional Autonoma de Mexico
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-013-0450-7
• 发表日期: 2014
• 页码: 453-482
• 关键词: chern classes; INVARIANTS; FORMULA; numbers

摘要

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 L cycles of Z; and vice versa: The L 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.