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トポロジー火曜セミナー
過去の記録 ～10/03｜次回の予定｜今後の予定 10/04～
| 開催情報 | 火曜日 17:00～18:30 数理科学研究科棟(駒場) 056号室 |
|---|---|
| 担当者 | 河澄 響矢, 北山 貴裕, 逆井卓也 |
| セミナーURL | http://park.itc.u-tokyo.ac.jp/MSF/topology/TuesdaySeminar/index.html |
2018年05月15日(火)
17:00-18:30 数理科学研究科棟(駒場) 056号室
Tea: Common Room 16:30-17:00
岡 睦雄 氏 (東京理科大学)
超曲面混合特異点理論とある予想 (JAPANESE)
Tea: Common Room 16:30-17:00
岡 睦雄 氏 (東京理科大学)
超曲面混合特異点理論とある予想 (JAPANESE)
[ 講演概要 ]
Consider a real algebraic variety of real codimension 2 defined by $V:=\{g(\mathbf x,\mathbf y)=h(\mathbf x,\mathbf y)=0\}$ in $\mathbb C^n=\mathbb R^n\times \mathbb R^n$. Put $\mathbf z=\mathbf x+i\mathbf y$ and consider complex valued real analytic function $f=g+ih$. Replace the variables $x_1,y_1\dots, x_n,y_n$ using the equality $x_j=(z_j+\bar z_j)/2,\, y_j=(z_j-\bar z_j)/2i$. Then $f$ can be understood to be an analytic functions of $z_j,\bar z_j$. We call $f$ a mixed function. In this way, $V=\{f(\mathbf z,\bar{\mathbf z})=0\}$ and we can use the techniques of complex analytic functions and the singularity theory developed there. In this talk, we explain basic properties of the singularity of mixed hyper surface $V(f)$ and give several open questions.
Consider a real algebraic variety of real codimension 2 defined by $V:=\{g(\mathbf x,\mathbf y)=h(\mathbf x,\mathbf y)=0\}$ in $\mathbb C^n=\mathbb R^n\times \mathbb R^n$. Put $\mathbf z=\mathbf x+i\mathbf y$ and consider complex valued real analytic function $f=g+ih$. Replace the variables $x_1,y_1\dots, x_n,y_n$ using the equality $x_j=(z_j+\bar z_j)/2,\, y_j=(z_j-\bar z_j)/2i$. Then $f$ can be understood to be an analytic functions of $z_j,\bar z_j$. We call $f$ a mixed function. In this way, $V=\{f(\mathbf z,\bar{\mathbf z})=0\}$ and we can use the techniques of complex analytic functions and the singularity theory developed there. In this talk, we explain basic properties of the singularity of mixed hyper surface $V(f)$ and give several open questions.
