2
$\begingroup$

I have a confusion about the following proofenter image description here

Here it says the the transition function from $U_1$ to $U_0$ is multiplication by $x_{0/1}$. I don't understand what that means. My understanding the transition function should be a map from $\operatorname{Spec}(k[x_{0/1},1/x_{0/1}])$ to $\operatorname{Spec}(k[x_{1/0},1/x_{1/0}])$. I don't understand how is multipliction by$x_{0/1}$ is a map from $\operatorname{Spec}(k[x_{0/1},1/x_{0/1}])$ to $\operatorname{Spec}(k[x_{1/0},1/x_{1/0}])$.

  • 0
    That is wrong. The transition function replaces one of the variables by the inverse of the other. – 2017-02-11
  • 0
    @MarianoSuárez-Álvarez You mean the transition function is a map from $k[x_{0/1},1/x_{0,1}]$ to $k[x_{1/0},1/x_{1,0}]$ such that $x_{0/1}$ goes to $1/x_{1/0}$? – 2017-02-11
  • 1
    Honestly, that notation for variables makes me want to bury my head in the sand and wait for it to be gone... – 2017-02-11

0 Answers 0