Hello all.

Let $X_{p_0,\ldots,p_n}\subset\mathbb{P}^N=\mathbb{P}^N_{\mathbb{C}}$ be the sequence of blowing-ups $\pi:\mathrm{Bl}_{p_0,\ldots,p_n}\longrightarrow\mathbb{P}^n$ along $n+1$ points of $\mathbb{P}^n$ (maybe infinitely near points), embedded by very ample divisor $H_X\sim d\pi^{\ast}(H_{\mathbb{P}^4})-E_1-\cdots - E_n$ ($E_1,\ldots,E_n$ the exceptional divisors, $H_{\mathbb{P}^4}\in|\mathcal{O}_{\mathbb{P}^4}(1)|$, $d\geq 1$).

If $p_0' ,\ldots, p_n'$ is another list of $n+1$ points that produces $X_{p_0',\ldots,p_n'}$ as above, is true that $X_{p_0,\ldots,p_n}, X_{p_0',\ldots,p_n'}$ are projectively equivalent ?

Thanks.