How can a torus $T^n$ acts on the projective space $\mathbb{P}^n=\mathbb{P}(\mathbb{C}^{n+1})$?
Is it possible or I'm doing a mistake because I need to consider $\mathbb{P}^{n-1}$ ?
Thanks
How can a torus $T^n$ acts on the projective space $\mathbb{P}^n=\mathbb{P}(\mathbb{C}^{n+1})$?
Is it possible or I'm doing a mistake because I need to consider $\mathbb{P}^{n-1}$ ?
Thanks
$(t_1,...,t_n)\in (\mathbb C^*)^n$ sending $[x_0,...,x_n]\in \mathbb P^n$ to $[x_0,t_1x_1,...,t_nx_n]\in \mathbb P^n$ defines an action of $(\mathbb C^*)^n$ on $\mathbb P^n$.