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Finite ๐-determinacy of generic homogeneous map germs in โ<sup>3</sup>
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- Farnik Michaล
- Faculty of Mathematics and Computer Science Jagiellonian University
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- Jelonek Zbigniew
- Instytut Matematyczny Polska Akademia Nauk
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- Ruas Maria Aparecida Soares
- Departamento de Matemรกtica ICMC-USP
Bibliographic Information
- Other Title
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- Finite A-determinacy of generic homogeneous map germs in โยณ
- Finite $\mathcal{A}$-determinacy of generic homogeneous map germs in $\mathbb{C}^3$
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Description
<p>Denote by ๐ป(๐1, ๐2, ๐3) the set of all homogeneous polynomial mappings ๐น = (๐1, ๐2, ๐3) : โ3 → โ3, such that deg ๐๐ = ๐๐. We show that if gcd(๐๐, ๐๐) ≤ 2 for 1 ≤ ๐ < ๐ ≤ 3 and gcd(๐1, ๐2, ๐3) = 1, then there is a non-empty Zariski open subset ๐ ⊂ ๐ป(๐1, ๐2, ๐3) such that for every mapping ๐น ∈ ๐ the map germ (๐น, 0) is ๐-finitely determined. Moreover, in this case we compute the number of discrete singularities (0-stable singularities) of a generic mapping (๐1, ๐2, ๐3): โ3 → โ3, where deg ๐๐ = ๐๐.</p>
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 73 (1), 211-220, 2021
The Mathematical Society of Japan
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Details ่ฉณ็ดฐๆ ๅ ฑใซใคใใฆ
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- CRID
- 1390849931331350656
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- NII Article ID
- 130007973749
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- NII Book ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL BIB ID
- 031231383
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- Text Lang
- en
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- Data Source
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- JaLC
- NDL Search
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed