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One-parameter families of homeomorphisms, topological monodromies, and foliations. (English) Zbl 1376.32015

Summary: The homological monodromy of a degeneration whose singular fiber has at most normal crossings was described by C. H. Clemens. In his work, local monodromies were described in detail. It is actually a classical result that the local monodromy around a node is a Dehn twist. For higher-dimensional case, we describe local monodromies alternatively: On a local smooth fiber of dimension \(n \geq 2\), we construct \(n+1\) singular foliations and then describe the action of the local monodromy on each leaf. Here the \(i\)th singular foliation is used for describing its action on the \(i\)th face of the boundary of a local smooth fiber.

MSC:

32G05 Deformations of complex structures
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