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Let $S=k[x_0,x_1,x_2]$, $k$ an algebraically closed field and $ S_d=k[x_0^d,x_0^{d-1}x_1,\ldots,x_2^{d-1}x_1, x_2^d]$. $\mathbb{P}S_d $ is identified with the projective space $\mathbb{P}^{N_d} $, where $N_d={2+d\choose 2}-1 $. I want to know construction of $\mathbb{P}S_d $.

Thank you.

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The notation is wrong. The correct one is $\mathrm{Proj}$. See en.wikipedia.org/wiki/Proj_construction and any book introducing algebraic geometry. –  Martin Brandenburg Feb 19 at 15:56

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