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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.21518 |
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| _version_ | 1866918263787618304 |
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| author | Saji, Kentaro Umehara, Masaaki Yamada, Kotaro |
| author_facet | Saji, Kentaro Umehara, Masaaki Yamada, Kotaro |
| contents | We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More concretely, a subset of Euclidean space is called a global main-analytic set if it can be described, up to a set of smaller Hausdorff dimension, as part of the zero set of a single real-analytic function, referred to as its main-analytic function.
In this paper, we propose a general framework for constructing main-analytic functions by a method based on explicit resultant computations. In particular, we provide explicit formulas for the main-analytic functions associated with the standard maps of wave-front singularities of types A, D and E. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21518 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit analytic functions defining the images of wave-front singularities Saji, Kentaro Umehara, Masaaki Yamada, Kotaro Differential Geometry Primary 32B20, Secondary 58C25 We give explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. Such functions are realizations of the main-analytic sets in the sense of Ishikawa-Koike-Shiota (1984). More concretely, a subset of Euclidean space is called a global main-analytic set if it can be described, up to a set of smaller Hausdorff dimension, as part of the zero set of a single real-analytic function, referred to as its main-analytic function. In this paper, we propose a general framework for constructing main-analytic functions by a method based on explicit resultant computations. In particular, we provide explicit formulas for the main-analytic functions associated with the standard maps of wave-front singularities of types A, D and E. |
| title | Explicit analytic functions defining the images of wave-front singularities |
| topic | Differential Geometry Primary 32B20, Secondary 58C25 |
| url | https://arxiv.org/abs/2512.21518 |