English

Blow-analytic retraction onto the central fibre

Complex Variables 2016-09-07 v1

Abstract

Let X be a complex analytic space and let f:X -> C be a proper complex analytic function with nonsingular generic fibres. By adapting the blowanalytic methods of Kuo we construct a retraction of a neighbourhood of the central fibre f^{-1}(0) onto f^{-1}(0). Our retraction is defined by the flow of a real analytic vector field on an oriented real analytic blow-up of X. Then we describe in terms of this blow-up the associated specialization map and local Milnor fibrations. The method also works in real analytic category.

Keywords

Cite

@article{arxiv.math/9701221,
  title  = {Blow-analytic retraction onto the central fibre},
  author = {Adam Parusinski},
  journal= {arXiv preprint arXiv:math/9701221},
  year   = {2016}
}
R2 v1 2026-07-22T17:56:36.736Z