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I have found in Mathoverflow Kähler cone of $\mathbb{C}P^n\sharp\mathbb{C}P^n$ that :

Let $X=\mathbb{C}P^n\sharp\mathbb{C}P^n$ be the blowing up at a point. The Kähler 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!

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    $\begingroup$ @Dima I just have searched this book and find the proof. Thank you for your comment $\endgroup$
    – Faith
    Commented Sep 27, 2017 at 8:09
  • $\begingroup$ The blowup of $\mathbb{CP}^n$ at a point is diffeomorphic to $\mathbb{CP}^n\#\overline{\mathbb{CP}^n}$, not $\mathbb{CP}^n\#\mathbb{CP}^n$. For $n$ even, the two spaces are not even homotopy equivalent. $\endgroup$
    – Michael Albanese
    Commented Sep 27, 2017 at 15:58

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