Milnor Fiber Consistency via Flatness

Fuente: arXiv
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1. Verfasser: Hof, Alex
Format: Preprint
Veröffentlicht: 2022
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_version_ 1866915180022071296
author Hof, Alex
author_facet Hof, Alex
contents We describe a new algebro-geometric perspective on the study of the Milnor fibration and, as a first step toward putting it into practice, prove powerful criteria for a deformation of a holomorphic function germ to admit a stratification on its domain partially satisfying the Thom condition and, more generally, to respect the Milnor fibration of the original germ in an appropriate sense. As corollaries, we obtain a method of partitioning the space of homogeneous polynomials of a fixed degree into finitely many locally closed subsets such that the fiber diffeomorphism type of the Milnor fibration is constant along each subset and a criterion under which deformations of a function with critical locus a complete intersection will be well-behaved.
format Preprint
id arxiv_https___arxiv_org_abs_2212_12807
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Milnor Fiber Consistency via Flatness
Hof, Alex
Algebraic Geometry
Complex Variables
14B07 (Primary) 32S30, 58K60 (Secondary)
We describe a new algebro-geometric perspective on the study of the Milnor fibration and, as a first step toward putting it into practice, prove powerful criteria for a deformation of a holomorphic function germ to admit a stratification on its domain partially satisfying the Thom condition and, more generally, to respect the Milnor fibration of the original germ in an appropriate sense. As corollaries, we obtain a method of partitioning the space of homogeneous polynomials of a fixed degree into finitely many locally closed subsets such that the fiber diffeomorphism type of the Milnor fibration is constant along each subset and a criterion under which deformations of a function with critical locus a complete intersection will be well-behaved.
title Milnor Fiber Consistency via Flatness
topic Algebraic Geometry
Complex Variables
14B07 (Primary) 32S30, 58K60 (Secondary)
url https://arxiv.org/abs/2212.12807