Vanishing cycles and singularities of meromorphic functions

Details Vanishing cycles and singularities of meromorphic functions Vanishing cycles and singularities of meromorphic functions

1999-05-19

arxiv.org/abs/math/9905108v1

Contemporary Math. 354 (2004), 277-289.

Mathematics

Algebraic Geometry

16 pages, Latex2e

Scientific paper

We study vanishing cycles of meromorphic functions. This gives a new and unitary point of view, extending the study of the topology of holomorphic germs -- as initiated by Milnor in the sixties -- and of the global topology of polynomial functions, which has been advanced more recently. We define singularities along the poles with respect to a certain (weak) stratification and prove local and global bouquet structure in case of isolated singularities. In general, splitting of vanishing homology at singular points and global Picard-Lefschetz phenomena occur.

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