Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917776371744768 |
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| author | Kerner, Dmitry Mendes, Rodrigo |
| author_facet | Kerner, Dmitry Mendes, Rodrigo |
| contents | Let X_o be a weighted-homogeneous complete intersection germ in (R^N,o) or (C^N,o), with arbitrary singularities, possibly non-reduced. Take the foliation of the ambient space by weighted-homogeneous real arcs, \ga_s.
Take a deformation of X_o by higher order terms, X_t. Does the foliation \ga_s deform compatibly with X_t? We identify the ``obstruction locus", Σin X_o, outside of which such a deformation does exist, and possesses exceptionally nice properties.
Using this deformed foliation we construct a contact trivialization of the family of defining equations by a homeomorphism that is real analytic (resp. Nash) off the origin, differentiable at the origin, whose presentation in weighted-polar coordinates is globally real-analytic (resp. globally Nash), and with controlled Lipschitz/C^1-properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS Kerner, Dmitry Mendes, Rodrigo Algebraic Geometry Complex Variables Metric Geometry Let X_o be a weighted-homogeneous complete intersection germ in (R^N,o) or (C^N,o), with arbitrary singularities, possibly non-reduced. Take the foliation of the ambient space by weighted-homogeneous real arcs, \ga_s. Take a deformation of X_o by higher order terms, X_t. Does the foliation \ga_s deform compatibly with X_t? We identify the ``obstruction locus", Σin X_o, outside of which such a deformation does exist, and possesses exceptionally nice properties. Using this deformed foliation we construct a contact trivialization of the family of defining equations by a homeomorphism that is real analytic (resp. Nash) off the origin, differentiable at the origin, whose presentation in weighted-polar coordinates is globally real-analytic (resp. globally Nash), and with controlled Lipschitz/C^1-properties. |
| title | Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS |
| topic | Algebraic Geometry Complex Variables Metric Geometry |
| url | https://arxiv.org/abs/2409.09764 |