Milnor Fiber Consistency via Flatness
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866915180022071296 |
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| 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 |