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齋藤 幸子
サイトウ サチコ SAITO Sachiko 所 属 旭川校 職 名 教授 |
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| 言語種別 | 英語 |
| 発行・発表の年月 | 2022/03/26 |
| 形態種別 | その他論文 |
| 標題 | A note on Newton non-degeneracy of mixed weighted homogeneous polynomials |
| 執筆形態 | 共著第一著者 |
| 掲載区分 | 国外 |
| 出版社・発行元 | arXiv:2107.08691 |
| 総ページ数 | 11 |
| 担当区分 | 筆頭著者,責任著者 |
| 著者・共著者 | Sachiko Saito, Kosei Takashimizu |
| 概要 | A mixed polynomial f(z, z¯) is called a mixed weighted homogeneous polynomial (Definition 11) if it is both radially and polar weighted homogeneous. Let f be a mixed weighted homogeneous polynomial with respect to a strictly positive radial weight vector P and a polar weight vector Q. Suppose that f is Newton non-degenerate over a compact face ∆(P) and f is polar weighted homogeneous of non-zero polar degree with respect to Q. Then we can show that f : C^∗^n → C has no mixed critical points. Moreover, if we assume that f^{−1}(0) ∩ C^∗^n \neq \emptyset, then we can show that f : C^∗^n → C is surjective. In other words, in this case, Newton non-degeneracy over a compact face ∆(P) implies strong Newton non-degeneracy over ∆(P) (Proposition 18). This is a well-known fact (see [2], Remark 4). The main purpose of this note is to give clear formulations of Newton non-degeneracy and strong Newton non-degeneracy and prove Proposition 18 in detail. |
| arXiv ID | arXiv:2107.08691 |