I have found in Mathoverflow [Kahler cone of $\mathbb{C}P^n\sharp\mathbb{C}P^n$ ] 1 that :

Let $X=\mathbb{C}P^n\sharp\mathbb{C}P^n$ be the blowing up at a point. The K$\ddot{a}$hler cone of $X$ is $$\mathcal{P}\backsimeq \{ a,b\in \mathbb{R}^2| a>0,b>0,a>b\}$$ There the author presents the proof of the above isomorphism, however I cannot understand. Can anyone offer more explicit proof or some references of this problem? Thank you very much!