next up previous
Next: About this document ...

    

鐃緒申鐃緒申鐃� II 鐃緒申鐃緒申 No.12

鐃緒申鐃緒申鐃塾テ￥申鐃緒申:

\fbox{多項式写像の像}

鐃緒申鐃� 12.1   鐃緒申鐃重�鐃緒申鐃緒申 $V$ 鐃塾削申標鐃緒申 $A(V)$ 鐃塾ワ申鐃叔ワ申鐃緒申 $I$ 鐃緒申与鐃緒申鐃緒申譴随申鐃緒申鐃�

\begin{displaymath}\{x\in V; p(x)=0 \qquad (\forall p\in I)\} \end{displaymath}

鐃熟わ申呂鐃緒申鐃緒申的鐃緒申鐃緒申任鐃緒申襦ｏ申鐃緒申鐃緒申 ($V=k^n$ 鐃塾誌申鐃緒申同鐃粛に￥申) $V(I)$ 鐃夙わ申鐃緒申鐃緒申

鐃緒申鐃緒申 12.1   鐃緒申鐃重�鐃緒申鐃緒申 $V,W$ 鐃塾間わ申多鐃準式鐃緒申鐃緒申 $f$ 鐃緒申与鐃緒申鐃緒申鐃銃わ申鐃緒申箸鐃緒申襦ｏ申鐃緒申里箸鐃緒申鐃� $f$ 鐃緒申鐃出縁申鐃緒申鐃緒申愎鐃緒申弔僚鐃銃縁申鐃緒申鐃緒申鐃�(鐃瞬逸申鐃緒申鐃潤し鐃緒申) $\phi$ 鐃塾核わ申 $I$ 鐃夙わ申鐃緒申鐃夙￥申 鐃緒申鐃塾わ申鐃夙わ申鐃緒申鐃緒申立鐃縦￥申
1.

\begin{displaymath}I=\{p \in A(W); p\vert\operatorname{Image}(f)=0 \} \end{displaymath}

2.
$V(I)$ 鐃緒申 $\operatorname{Image}(f)$ 鐃緒申鐃緒申分鐃緒申鐃緒申箸鐃緒申憧泙鐃� $W$ 鐃緒申鐃緒申鐃重�鐃緒申鐃緒申里鐃緒申鐃緒申鐃� 鐃叔常申鐃塾わ申里任鐃緒申襦� (Zariski 鐃緒申鐃緒申慮鐃緒申佞任鐃緒申鐃緒申个鐃緒申鐃緒申 $V(I)$ 鐃緒申 $\operatorname{Image}(f)$ 鐃緒申(Zariski鐃緒申鐃緒申亡悗鐃緒申鐃�) 鐃緒申鐃緒申任鐃緒申鐃夙醐申鐃獣てもお鐃淑わ申鐃緒申鐃夙でわ申鐃暑。)

鐃緒申鐃緒申泙任里箸鐃緒申鐃緒申鐃緒申単鐃緒申表鐃祝まとわ申鐃夙￥申鐃緒申鐃塾よう鐃淑駈申鐃祝なる。

鐃緒申鐃緒申 鐃緒申鐃緒申鐃緒申鐃緒申鐃�
鐃瞬ワ申痢廚鐃緒申弍鐃�
多鐃準式鐃緒申 $k[X_1,X_2,\dots,X_n]$ n鐃緒申鐃緒申鐃緒申鐃緒申 $k^n$ 鐃塾削申標鐃緒申
鐃緒申 $k$ 鐃緒申泙鐃緒申 $R$ 鐃緒申鐃重�鐃緒申鐃緒申 $V$ 鐃塾削申標鐃緒申 A(V)
$R$ 鐃塾ワ申鐃叔ワ申鐃緒申 $I$ $V$ 鐃緒申鐃緒申鐃重�鐃緒申分鐃緒申鐃緒申(Zariski 鐃縦緒申鐃緒申) $F$ 鐃緒申
  鐃緒申鐃緒申鐃緒申砲覆鐃舜随申鐃緒申鐃緒申
鐃緒申余鐃緒申 $R/I$ $V$ 鐃緒申鐃緒申鐃重�鐃緒申分鐃緒申鐃緒申 $F$ 鐃塾削申標鐃緒申 A(F)
$k$-鐃緒申同鐃緒申 $\phi:A(W)\to A(V)$ 鐃緒申鐃重�鐃緒申鐃緒申隆屬鐃渋随申犲逸申鐃緒申鐃� $f={}^a\phi:V\to W$
鐃緒申同鐃緒申鐃塾鰹申 $\operatorname{Ker}(\phi)$ 多鐃準式鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申 Zariski 鐃緒申鐃緒申 $\overline{f(V)}$
鐃緒申鐃緒申鐃緒申鐃竣わ申鐃出縁申
$R$ 鐃緒申鐃緒申鐃緒申鐃淑駈申鐃緒申鐃緒申鐃緒申鐃緒申鐃� $V$ 鐃緒申鐃緒申弔慮鐃緒申鐃淑わ申鐃緒申鐃重�鐃緒申鐃緒申鐃渋緒申鐃緒申任鐃緒申鐃�
$R$ 鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申鐃述わ申鐃緒申鐃� $V$ 鐃熟駕申鐃緒申鐃緒申鐃緒申的鐃緒申鐃緒申

鐃緒申鐃緒申表鐃熟わ申鐃淑わ申鐃緒申泙鐃緒申覆鐃塾で￥申鐃緒申密鐃祝はわ申鐃緒申鐃緒申鐃駿の常申錣�鐃淑わ申鐃夙削申鐃緒申鐃塾刻申鐃旬わ申 鐃出縁申鐃緒申鐃淑わ申鐃獣わ申鐃所、鐃緒申鐃緒申鐃緒申鐃縦わ申鐃緒申鐃緒申鐃盾あ鐃暑。 鐃緒申鐃緒申鐃塾詳細につわ申鐃銃はわ申鐃曙ぞ鐃緒申硫鐃緒申鐃緒申鐃緒申鐃緒申鐃薯参照わ申鐃曙た鐃緒申鐃緒申 鐃緒申鐃緒申的鐃祝は￥申鐃緒申鐃緒申的鐃淑ワ申鐃潤ー鐃緒申鐃薯うまわ申鐃夙っわ申鐃緒申鐃緒申鐃緒申聴鐃緒申鐃緒申鐃緒申鐃緒申里鐃緒申鐃� 鐃緒申鐃緒申鐃緒申鐃緒申鐃塾な常申鐃緒申鐃緒申弔鐃緒申鐃塾わ申鐃処い鐃緒申鐃緒申鐃緒申鐃緒申

鐃緒申鐃緒申 12.1   $A=\mbox{${\Bbb R}$ }[X,Y,Z]$ 鐃緒申鐃緒申 $A$ 鐃舜の環緒申同鐃緒申鐃緒申鐃緒申 $\phi$ 鐃緒申

\begin{displaymath}\phi(X)=XZ,\quad \phi(Y)=(YZ),\quad \phi(Z)=Z \end{displaymath}

鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃祝￥申$A$ 鐃塾ワ申鐃叔ワ申鐃緒申 $I$ 鐃緒申

\begin{displaymath}I=(X^2+Y^2-1) \end{displaymath}

鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申里箸鐃緒申鐃�
1.
$V(I)$ 鐃塾ワ申鐃緒申佞粒鐃緒申鐃緒申鐃書きなわ申鐃緒申鐃緒申
2.
$\psi=\pi\circ\phi: A \to A/I $ 鐃塾核わ申鐃緒申覆鐃緒申鐃緒申鐃� 鐃緒申鐃緒申鐃緒申 $\pi:A\to A/I$ 鐃熟種申鐃緒申鐃淑射縁申 ($p$ 鐃緒申鐃出わ申鐃銃わ申鐃塾ワ申鐃初ス $[p]$鐃緒申鐃出縁申鐃緒申鐃緒申鐃緒申鐃銃縁申鐃�)鐃叔わ申鐃暑。
3.
${}^a\psi$ 鐃緒申鐃緒申鐃塾鰹申鐃緒申鐃緒申颪�なわ申鐃緒申鐃緒申

鐃緒申鐃緒申 12.2   $B=\mbox{${\Bbb R}$ }[X,Y]$ 鐃緒申鐃緒申 $B$ 鐃舜の環緒申同鐃緒申鐃緒申鐃緒申 $\varphi$ 鐃緒申

\begin{displaymath}\varphi(X)=XY,\qquad \varphi(Y)=Y \end{displaymath}

鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申鐃祝￥申$B$ 鐃塾ワ申鐃叔ワ申鐃緒申 $J$ 鐃緒申

\begin{displaymath}J=(Y-X^2+1) \end{displaymath}

鐃緒申鐃緒申鐃緒申鐃緒申襦ｏ申鐃緒申里箸鐃緒申鐃�
1.
鐃緒申鐃緒申10.1 鐃祝なわ申辰鐃� ${}^a\varphi(S)$ 鐃薯グワ申佞暴颪�なわ申鐃緒申鐃緒申 鐃緒申鐃緒申鐃緒申鐃緒申

\begin{displaymath}S=\{ (x,y)\in \mbox{${\Bbb R}$}^2; x \in {\mbox{${\Bbb Z}$}}\text{ or } y \in {\mbox{${\Bbb Z}$}}\} \end{displaymath}

鐃叔わ申鐃暑。
2.
$V(J)$ 鐃塾ワ申鐃緒申佞粒鐃緒申鐃緒申鐃書きなわ申鐃緒申鐃緒申
3.
$\rho=\pi\circ\varphi: B \to B/J $ 鐃塾核わ申鐃緒申覆鐃緒申鐃緒申鐃� 鐃緒申鐃緒申鐃緒申 $\pi:B\to B/J$ 鐃熟種申鐃緒申鐃淑射縁申 ($p$ 鐃緒申鐃出わ申鐃銃わ申鐃塾ワ申鐃初ス $[p]$鐃緒申鐃出縁申鐃緒申鐃緒申鐃緒申鐃銃縁申鐃�)鐃叔わ申鐃暑。
4.
${}^a\rho$ 鐃緒申鐃緒申鐃塾鰹申鐃緒申鐃緒申颪�なわ申鐃緒申鐃緒申

鐃緒申鐃緒申1, 2 鐃夙わ申傍鐃緒申鐃緒申里曚鐃緒申鐃竣誌申鐃緒申鐃銃わ申鐃殉わ申鐃緒申鐃緒申鐃淑のわ申鐃緒申鐃春￥申 鐃緒申鐃緒申佞箸茲�鐃緒申鐃緒申戮討澆鐃夙わ申鐃緒申鐃緒申鐃緒申鐃緒申鐃緒申 鐃緒申鐃緒申法鐃�MuPAD 鐃淑どで実際にワ申鐃緒申佞鮓�てみわ申箸鐃獣とよい鐃緒申 MuPAD 鐃熟刻申鐃緒申鐃順か鐃緒申覆鐃� 

http://www.math.kochi-u.ac.jp/docky/kogi/
鐃叔ワ申鐃緒申鐃緒申鐃緒申鐃緒申匹任鐃緒申襦�
next up previous
Next: About this document ...

2001-07-24