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Let <em>X</em> be a smooth projective variety over an algebraically closed field <em>k</em>. We associate to <em>X</em> , in a functorial way, a multigraded k-algebra <em>G(X)</em>, called the global ring of <em>X</em> . We find some results when <em>dim X = 2</em>, and we explicitly determine the global ring in two particular cases.<br />