Approximate roots, toric resolutions and deformations of a plane branch
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- González Pérez Pedro Daniel
- Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Departamento de Álgebra, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid
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We analyze the expansions in terms of the approximate roots of a Weierstrass polynomial f ∈ C {x}[y], defining a plane branch (C,0), in the light of the toric embedded resolution of the branch. This leads to the definition of a class of (non-equisingular) deformations of a plane branch (C,0) supported on certain monomials in the approximate roots of f, which are essential in the study of Harnack smoothings of real plane branches by Risler and the author. Our results provide also a geometrical approach to Abhyankar's irreducibility criterion for power series in two variables and also a criterion to determine if a family of plane curves is equisingular to a plane branch.
収録刊行物
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 62 (3), 975-1004, 2010
一般社団法人 日本数学会
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詳細情報 詳細情報について
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- CRID
- 1390001205115318400
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- NII論文ID
- 10027870948
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 10764269
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
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- CiNii Articles
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